科学研究

学术交流

首页 >  科学研究 >  学术交流 >  正文
河南大学数学短期课程(共24学时)-Monge-Ampere方程及其应用
作者:    时间:2018-11-28 浏览次数:

  

课程名称:  Monge-Ampere方程及其应用

适用对象:研究生、青年教师

授课教师:马力教授(北京科技大学,鼎新人才计划,博士生导师)

授课时间123-1230日,每周一、周二、周四晚上19:00-21:00.

授课地点:数学与统计学院一楼报告厅

课程和内容简介

Monge-Ampere方程(和曲率流问题)是现代偏微分方程和几何分析里的基本内容。著名数学家Caffarelli由于在Monge-Ampere 方程方向的工作获得了Wolf奖;著名数学家Figalli由于在这个方向的工作在2018年获得了Fields奖。

本课程的主体内容有:

1. 平面凸曲线和曲线流介绍;

2. 凸曲面微分几何,等周问题;

3. 凸集合支撑函数,活动标架法;

 4. 凸曲面的几何有名定理Minkowski问题和Monge-Ampere方程;

5. Juergens

6.基本黎曼几何回顾;

7. 阿达玛定理;

8. Minkowski问题;

9.Calabi估计;

10.唯一性定理(Chern);

11.Bernstein型定理;

12. 曲率流问题和孤立子问题

参考书:

1. A.V.PogorelovThe Minkowski multidimensional problem, John Wiley& Sons, New York, 1978

2. Alessio FigalliThe Monge-Ampere equation and its applications, Zurich lectures in advanced mathematics, EMS, 2017.

马力教授简介:


Working and teaching experience:

2017/07–up to now; A2 Full Professor, The university of science and technology Beijing. 2010/09–2017/06 Distinguished professor, Henan Normal University, Henan. 1998/07– 2010/08; Full Professor, Tsinghua University, Beijing.

1991/07– 1998/06: Associate Professor, Tsinghua University, Beijing.

1995/09– 1997/06.: Lecturer: Rutgers University, New Brunswick, New Jersey, NJ 08903, USA.

1989/08– 1991/06.: Post-doctor, Beijing University, Beijing.

Editors-in-chief: Pure Mathematics, a Chinese Mathematical journal, 2010-2012.

Editors: 1. Annals of Global Analysis and Geometry, Springer.

2. Journal of Pseudo-Differential Operators and Applications (JPDOA), Birkhauser, Springer.

Affiliations: Refereeing papers for journals including: Chinese Annals of Math., Acta Math.Sinica, Scientia in China, CPAM, CPAA, IMRN, Math.and computer modelling, Comm.Math.Helv.,AGAG,JMAA, Nonlinear Analysis, etc.

Honors and grants:

Winner of research award of He Yingdong for Young teachers: 1999-2000, National Education Ministry of China.

Research Fund a member of a key Project of nation science and technology ministry of of China: ”Nonlinear elliptic and parabolic equations” (10631020): 2006.1-2010,12.) the Na- tional Natural Science Foundation of China (No. 11271111), (SRFDP 20090002110019)(2010.1- 2012.12) and (SRFDP 20060003002) (2006.1-2008.12) for the doctoral program of higher education from the ministry of education. The national natural science foundation (di- rector fund, 1997.1-1998,12) and The national natural science foundation (youth fund,

1993.1-1995.12) 1

Visiting professors:

Stanford University (2018,6-7), California University, Santa Barbara (2018,5-6), Min- nesota University (2016,8,30-9,30), IHES, France (2014,6-8, 2010,7-9, 2006,4-7, 2002,8-10),Imperial College of London, England; University of Paris-Sud, University of Paris-6&7, University of Paris-13, University of Rouen, France; Toronto University, CRM Montreal Univ., Canada; NUS, Singapore; Chinese University of Hongkong, ETH-Zurich, Swissland; ICTP, and Rome (I) University,Italy; Sydney University,Australia; Minster University, Potsdam University, Germany; Kyoto University, Japan

Invited speaker : Cornell University (1995.11), New York University (1995.10), New York City University (1996.2), Northeastern University (1996.4), Yeshiva Univ. (August 6th, 2013).

Member : AMS, CMS, and CSIAM.

Organizer : 1. International conference of PDE and thieir applications (Wuhan Univ. April 5-9, 1999) 2. Summer school of geometric analysis and mathematical physics (Henan Normal Univ., July 24 to August 10th, 2015). 3. Summer school of Geometric analysis ( Northeastern Normal Univ., July 5th to 24th, 2016). 4. International conference of Geometric analysis (Jilin Univ., July 25 to July 29, 2016)

Reviewer : Math. Reviews (USA), Math. Abstracts (Germany), QS world university ranking.

Course taught: Calculus (USA), Linear Algebra (USA), Linear Functional Analysis (graduate course), Nonlinear Analysis (graduate course), Differential Geometry, Equations of Math. Physics, functional analysis, real variable theory, complex analysis, Riemannian geometry, etc.

Authors of Books:

1. A Concise Course in Differential Geometry, Tsinghua University Press, 2004.

2. Ricci-Hamilton Flow on Surfaces, Global Scientific Publishing, Singapore, 2004.

Publications (In the following, SCI=*): Published papers (*=SCI)

*132,Li, Jiaojiao; Ma, Li, Finite time blowup and global solutions of Euler type equa- tions in matrix geometry. J. Math. Phys. 59 (2018), no. 7, 072205, 9 pp. 35Q31 (35B44 76B03)

*131, Ma, Li, Liouville theorems, volume growth, and volume comparison for Ricci shrinkers. Pacific J. Math. 296 (2018), no. 2, 357-369. 53C21 (53C25 53C44)

*130, Ma, Li, Convexity and the Dirichlet problem of translating mean curvature flows. Kodai Math. J. 41 (2018), no. 2, 348-358. 53C44 (53C21 58J05)

*129, Cai, Miaomiao; Ma, Li, Moving planes for nonlinear fractional Laplacian equation with negative powers. Discrete Contin. Dyn. Syst. 38 (2018), no. 9, 4603-4615. 35R11 (35J60 58J05)

*128, Ma, Li, Harnack’s inequality and Green’s functions on locally finite graphs. Non- linear Anal. 170 (2018), 226-237. (Reviewer: Shoudong Man) 05C50 (31C05 31C20)

*127, Ma, Li; Witt, Ingo, Discrete Morse flow for Ricci flow and porous medium equa- tion. Commun. Nonlinear Sci. Numer. Simul. 59 (2018), 158-164. (Reviewer: Kin Ming Hui) 53C44 (35K55)

*126, Li, Jiaojiao; Ma, Li, Finite time blowup and global solutions of nonlinear heat equations in matrix geometry. J. Nonlinear Convex Anal. 18 (2017), no. 12, 2155-2162. 35K91 (35A01 35B44)

*125,Li Ma, Gradient estimates for a simple nonlinear heat equation on manifolds, applicable analysis, An International Journal, Volume 96, 2017 - Issue 2 pp.225-230

*124, Li Ma, Boundedness of solutions to GinzburgCLandau fractional Laplacian equa- tion, International Journal of Mathematics Vol. 27, No. 5 (2016) 1650048 (6 pages)

*123 Li Ma, Global Kaehler-Ricci flow on complete non-compact manifolds, Annali di Matematica (2016) 195:1011-1019

*122. Li Ma, Gap theorems for locally conformally flat manifolds. J. Differential Equa- tions 260 (2016), no. 2, 1414-1429

*121 Ma, Li; Liu, Baiyu; Blow up threshold for a parabolic type equation involving space integral and variational structure. Commun. Pure Appl. Anal. 14 (2015), no. 6, 2169-2183

*120 Liu, Baiyu; Ma, Li, Blow up threshold for the Gross-Pitaevskii system with com- bined nonlocal nonlinearities. J. Math. Anal. Appl. 425 (2015), no. 2, 1214-1224.

*119, Li Ma, I.Witt, Liouville theorem for the nonlinear Poisson equation on manifolds, J.Math.Anal. Appl., 416(2014)800-804

118, X.Z.Chen , L.Ma, X.W.Xu, Remarks on Q-curvature flows, Science China, 2(2014)183- 192, in Chinese.

*117, Li Ma, Liang Cheng, A Nonlocal area preserving curve flow, Geom. Dedicata (2014) 171:231-247

*116, B.Y. Liu, Li Ma, Invariant sets and the blow up threshold for a nonlocal equation

of parabolic type, Nonlinear Analysis, 110(2014)141-156, http://dx.doi.org/10.1016/j.na.2014.08.00

*115, Li Ma, Eigenvalue Estimates and L1 Energy on Closed Manifolds, Acta Mathe- matica Sinica, English Series, October 2014, Volume 30, Issue 10, pp 1729-1734,

*114, Li Ma, L.Cheng, Yamabe flow and Myers type theorem, Journal of Geom. Anal., 24(2014)246-270.

*113,Li Ma, A.Q.Zhu, Injectivity radius bound of Ricci flow with positive Ricci curva- ture and applications, Front. Math. China 2013, 8(5): 1129-1137 DOI 10.1007/s11464- 013-0296-8

*112 Baiyu Liu, Li Ma, Symmetry results for elliptic Schrodinger systems on half spaces, J. Math. Anal. Appl. 401 (2013) 259-268

*110, Li Ma, Convergence of Ricci flow on R2 to the plane, Differential Geometry and its Applications 31 (2013) 388-392

*109, Li Ma, J.Wang, Sharp Threshold of the GrossCPitaevskii Equation with Trapped

Dipolar Quantum Gases, Canad. Math. Bull. Vol. 56 (2), 2013 pp. 378-387 http://dx.doi.org/10.41

2011-181-2

*108, Li Ma, L.Cheng, Global solutions to norm-preserving non-local flows of porous media type, Proceedings of the Royal Society of Edinburgh, 143A, 871-880, 2013

*107, Li Ma, Remarks on compact shrinking Ricci solitons of dimension four, C. R. Acad. Sci. Paris, Ser. I 351 (2013) 817-823

*106, Li Ma, X.Y.Wang, Kato inequality and Ginzburg-landau equation in locally finite graphs, Science China, Mathematics, April 2013 Vol. 56 No. 4: 771-776 doi: 10.1007/s11425-013-4577-1.

*105, Li Ma, global existence and blow-up for parabolic equations with critical exponent, Comm. Pure Appl.Anal., Volume 12, Number 2, March 2013 pp. 1103-1110.

*104, Li Ma, global existence and blow-up for classical parabolic equations, Chinese Ann. Math.,34B(4), 2013, 587-592 DOI: 10.1007/s11401-013-0778-8.

*103, Li Ma, J.Wei, Stability of the Lichnerowicz equation, Journel Math.Pure Appl., 99 (2013) 174-186.

*102, Li Ma, Y.Sun, X.Tang, Heat flow method to the Lichnerowicz equations, ZAMP, 63(2012)261-270.

*101, Li Ma, L.Cheng, A.Q.Zhu, Extension of Yamabe flow on complete Riemannian manifolds, Bull. Sci.Math., 136(2012) 882-891.

*100 Baiyu Liu, Li Ma, symmetry results for decay solutions of semilinear elliptic sys- tems, Nonlinear Analysis, 75(2012)3167-3177.

*99, Li Ma, M. Vicente, Remarks on scalar curvature of Yamabe solitons, Ann Glob Anal Geom., (2012) 42:195-205

*98, Y.Du, Li Ma, A Liouville theorem for conformal Gaussian curvature type equations in R2, Calc. Var. PDE, 43(2012)485-505

*97,Li Ma, Anqiang Zhu, On a length preserving curve flow, Monatshefte fur Mathe- matik: Volume 165, Issue 1 (2012)57-78

96, Li Ma, Liouville Type Theorems for Lichnerowicz Equations and Ginzburg-Landau Equation: Survey,Advances in Pure Mathematics, 2011, 1, 99-104

*95, Li Ma, Liang Cheng, Properties of complete non-compact Yamabe solitons, Ann Glob Anal Geom (2011) 40:379-387

*94. Li Ma, Xingwang Xu, Ricci flow with hyperbolic warped product metrics, Math. Nachr. 284, No. 5-6, 739-746 (2011)

*93.Li Ma, Pei cao, The threshold for the focusing Gross-Pitaevskii equation with Trapped Dipole quantum Gases, J. Math. Anal. Appl. 381 (2011) 240-246

*92, Li Ma, Expanding Ricci solitons with pinched Ricci curvature, KODAI MATH. J. 34 (2011), 140-143

*91 Li Ma, Z.M.Guo, Finite Morse index steady states of van der Waals force driven thin film equations, J. Math. Anal. Appl. 368 (2010) 559-572

*90. Li Ma, Liouville type theorem and uniform bound for the Lichnerowicz equation and the GinzburgCLandau equation, C. R. Acad. Sci. Paris, Ser. I 348 (2010) 993-996

*89, Li Ma, B.-W.Schulze, Blow-up Theory for the Coupled L2-Critical Nonlinear Schrodinger System in the Plane, Milan Journal of Math. Vol. 78 (2010) 591-601.

*88, Li Ma, Shenghua Du, Extension of Reilly formula with applications to eigenvalue estimates for drifting Laplacians, C. R. Acad. Sci. Paris, Ser. I 348 (2010) 1203-1206

*87 Li Ma, Baiyu, Liu, Symmetry Results for decay solutions of Elliptic Systems in the whole Space, Advances in Mathematics 225 (2010) 3052-3063.

86 Li Ma, W.-B.Schulze, Operators on Manifolds with Conical Singularities, Journal of Pseudo-Differential Operators and Applications, (2010) 1:55-74

*85 Li Ma, Baiyu, Liu, Symmetry Results for classical solutions of Monge-Ampere systems on a bounded planar domain, JMAA, 369(2010)678-685.

84 Liang Cheng, Li Ma, REPORT ON THE Lp NON-LOCAL FLOW AND ITS APPLI-

CATION TO POPULATION MODEL, The 9th Inter. Conf. on Elect. business Macau, November 30, December 4, 2009. pp1103-1105.

*83 Li Ma, Haihong Liu, On energy stability for the coupled nonlinear wave  and Schrodinger systems, Nonlinear Analysis,72 (2010) 4541-4550

*82 Li Ma, Baiyu Liu, Q-curvature flow with indefinite nonlinearity, C. R. Acad. Sci. Paris, Ser. I 348 (2010) 403-406

*81 Li Ma, Liang Cheng, On the conditions to control the curvature tensors of Ricci flow, Ann Glob Anal Geom., 37(2010)403-411.

*80 Li Ma, Jie Zhou, Chern-Simons invariants and isometric immersions, Monatshefte fur Mathematik, 159(2010)361-378.

*79 Ma, Li; Hong, Min-Chun, Curvature flow to the Nirenberg problem. Arch. Math. (Basel) 94 (2010), no. 3, 277-289.

*78 Li Ma, Dezhong Chen, Remarks on complete non-compact gradient Ricci expanding solitons, KODAI MATH. J. 33 (2010), 173-181

*77 Li Ma, J. Wang,Inhomogeneous Problem for the Ginzburg-Landau Equation on Two Dimensional Compact Manifolds, Dynamics of PDE, Vol.7, No.2, 175-185, 2010

*76 Li Ma, Pei Cao, Imhomogenous initial-boundary problem for the Hartree type equation, JOURNAL OF MATHEMATICAL PHYSICS 51, 023516(2010)

75 Baiyu Liu, Li Ma, L2 p-forms and Ricci flow with bounded curvature on manifolds. The 9th Inter. Conf. on Elect. business Macau, November 30, December 4, 2009. pp1114- 1118.

*74 Li Ma, Lin Zhao, Energy stability for the time-dependent Hartree equation with positive energy, J. Math. Anal. Appl. 362 (2010)114-124.

*73.Li Ma, Xianfa Song, Lin Zhao, New Monotonicity Formulae for Semi-linear Elliptic and Parabolic Systems, Chin. Ann. Math. 31B(3), 2010, 411C432

*72. Li Ma, Lin Zhao, Classification of positive solitary solutions of the nonlinear Choquard equation, Arch. Rational Mech. Anal. 195 (2010) 455-467,

*71 Li Ma, Cheng Liang, non-local heat flows and gradient estimates on closed mani- folds, J. Evol. Equ. 9 (2009), 787C807.

*70. Li Ma, Xingwang Xu,uniform bound and a non-existence result for Lichnerowicz equation in the whole n-space, C.R.Mathematique, ser.I,347(2009)805-808

*69. Li Ma, Three remarks on mean fields equation, Pacific Journal of Math., 242(2009)167- 171

*68. Li Ma, Baiyu, Liu, Convex eigenfunction of a drifting Laplacian operator and the fundamental gap, Pacific Journal of Math., 240(2009)343-361.

*67. Li Ma, Xianfa Song, Lin Zhao,On global rough solutions to a nonlinear Schrodinger system, Glasgow Mathematical Journal, 51(2009)499-511.

*66. Li Ma, Anqiang Zhu, Nonsingular Ricci flow on a noncompact manifold in dimen- sion three, C.R.Mathematique, ser.I,137(2009)185-190.

*65. Li Ma, Dezhong Chen, Radial symmetry and uniqueness of non-negative solutions to an integral system, Mathematical and Computer Modelling, 49 (2009)379-385

*64. Li Ma,Lin Zhao, On energy stability for the coupled nonlinear Schrodinger system, Z. Angew Math.Phys., 60(2009)774-784

63. Li Ma, Baiyu Liu,Convexity of first eigenfunction of drifting Laplacian operator and its application, New York Journal of Mathematics, 14(2008)393-401

*62. Li Ma, Congming Li, Uniqueness of positive bound states to Schrodinger systems with critical exponents, SIAM Journal on Mathematical Analysis, Vol. 40, No. 3, pp. 1049-1057,2008.

*61. Li Ma and Lin Zhao, Uniqueness of ground states of some coupled nonlinear Schrodinger systems and their application, Journal of Diff. Equations, 245(2008)2551- 2565.

*60. Li Ma and Lin Zhao, Sharp thresholds of blow-up and global existence for the coupled nonlinear Schrodinger system, Journal of Mathematical Physics, 49, 062103(2008).

*59. Li Ma and Lin Zhao, Regularity for weak positive solution to semi-linear elliptic equations, Comm.Pure and Applied Analysis,7(3)(2008)631-643.

*58. Li Ma and Dezhong Chen, Radial Symmetry and Monotonicity Results for an Integral Equation, Journal of Mathematical Analysis and applications, 342 (2008) 943- 949.

*57. Li Ma, Lin Zhao, and Xiafa Song, Gradient estimate for the degenerate parabolic equation ut = ∆F (u) + H(u) on manifolds,J. Differential Equations, 244 (2008)1157-1177,

*56. Li Ma, Juncheng Wei, Properties of positive solutions of an Elliptic Equation with

negative exponents, J. Funct. Anal., 254(2008)1058-1087.

*55. Li Ma and Anqiang Zhu, Eigenvalues and lambda constants on Riemannian sub- mersions, Geometriae Dedicata, 129(2007)73-82.

*54. Li Ma and Lin Zhao, Blow-up of solutions to the nonlinear Schrodinger equations on manifolds, J. Math. Phys. 48, 053519 (2007) (15 pages) .

*53. Li Ma, Z.M.Guo, Asymptotic behavior of positive solutions of some quasi-linear elliptic problems, Journal of London Math. Soc. , 419-437(76)2007

*52. Li Ma, Xianzhe Dai, Mass under Ricci flow, Commun. Math. Phys. 274, 65-80 (2007),

*51. Li Ma, Chong Li, and Lin Zhao, Monotone solutions to a class of elliptic and diffusion equations, CPAA, 6(2007)237-246.

*50. Li MA and Dezhong Chen, Curve Shortening in a Riemannian Manifold, Annali math. pure and appl.,186(2007)663-684.

*49. Li Ma, Gradient estimates for a simple elliptic equation on complete non-compact Riemannian manifolds, Journal Functional Analysis, 241(2006)374-382.

*48. Li Ma, Yang Yang, L2 Forms and Ricci flow on Complete Non-compact manifolds,

GEOMETRIAE DEDICATA,119(2006)151-158.

*47. Li Ma, Eigenvalue monotonicity for the Ricci-Hamilton flow, AGAG, 29(2006)287- 292.

*46. Li MA, Dezhong Chen, Yang Yang, Some results for subelliptic equations, Acta. Math.Sinica. English series, 22(2006)1695-1704.

*46. Li Ma and D.Z.Chen, A Liouville type Theorem for an integral System, Comm. Pure and Appl. Anal., 5(2006)855-859.

*45. Li Ma, Some properties of non-compact complete Riemannian manifolds, Bull. Sci.Math.,130(2006)330-336.

*44. Li Ma and Dezhong, Chen, Examples for cross curvature flow on 3-manifolds, Calc. Var. and PDE., 26(2006)227-243.

*43. L.Ma, B-minimal sub-manifolds and their stability, Math. Nach, 279(2006)1597- 1601.

*42. Z.M.Guo, L.Ma, Asymptotic behavior of positive solutions of some quasi-linear elliptic problems, J.London Math.Soc., 2007.

*41, G.B. Li and Li Ma, Dirichlet problems of a quasi-linear elliptic system, Quarterly Journal of Mathematics, 56(2005)579-587.

*40. L.Ma, Y.Yang, A Remark on Soliton Equation of Mean Curvature Flow, Anais Acad. Brasileira de Ciencias, 76(2004)467-473.

39. L.Ma, and N.Su, Obstacle problem in scalar Ginzburg-Landau equation, Journal Partial Diff. Equations. 17(2004),49-56.

*38.Li MA and Dezhong Chen, System of Hermitian quadratic forms, Canadian Math. Bull., 47(1)(2004)73-81

*37. Ma Li, Su Ning, Existence, multiplicity, and Stability Results for Positive Solutions of Non-linear p-Laplacian Equations, Chinese Ann. Math.,25B(2004)275-286.

*36. N.Dancer, Du Yihong, and Ma Li, Asymptotic Behavior of elliptic equations, Pacific J. Math.,210(2003)215-228.

*35. L.Ma, Bifurcation in prescribed Mean Curvature Problem, Acta Math. Scientia, 22(2002)526-532

*34. Ma Li, Du Yihong, Some Remarks on De Giorgi conjecture, Proc. amer. math. soc., 131(2002)2415-2422.

*33. Ma Li, Du Yihong, Positive solutions of an elliptic equation on Rn, Journal Math.

Anal. Appl., 271(2002)409-425.

*32.Ma Li, Xu Xingwang, Positive solutions of a logistic equation on unbounded inter- vals, Proc. Amer. Math. Soc., 130(2002)2947-2958.

*31. Ma Li, Moduli space of special lagrangian submanifolds in almost Calabi-Yau manifolds, Anais Acad. Brasileira de Ciencias, Vol.73(1)(2001)pp1-5.

*30. Du.Yihong, Ma Li, Logistic equations on Rn by a squeezing method involving

boundary blow-up solutions, Journal of London Math. Soc., 64(2)(2001)107-124.

*29. Ma Li and J.Wei, Convergence For a Liouville Equation. Comment. Math. Helv., 76(2001)506-514.

28. Ma Li, Nirenberg’s problem in 90’s, in Differential Geometry of sub-manifolds, pp.171-177, U.Simon, etc, ed., 2000, World Scientific.

27. Li Ma, Harmonic maps versus Poisson Equations on Non-compact Riemannian Manifolds, System Sciences and Mathematics, 13(2000)333-336.

26. An Yinglian and Ma Li, On a Metric Fixed Point Theorem, Soochow Journal of Mathematics, Vol.26, 67-71(2000)

25. Ma Li , On the Existence of Solutions of Prescribing Scalar Curvature Problem, Tsukuba J. Math. 24, 133-137(2000).

24. Ma Li, Bifurcation in Some Partial Differential Equations With Critical Exponents, in Paul Erdos and His Mathematics, Janos Bolyai Mathematical Society, pp161-165, 1999.

23. An Yinglian and Ma Li, The Maximum Principle and the Yamabe Flow, in ”Partial Differential Equations and Their Applications”, World Scientific, Singapore, pp211-224, 1999.

*22.Ma Li , Minimal Graph Evolutions in the Hyperbolic Space, Acta Math. Sinica, New Series, 15(1999)371-374

*21. Bifurcation in Nirenberg’s Problem, C.R.Acad.Sci.Paris.t326,Serie I, p.583-588, 1998.

*20. Mountain pass on a Closed Convex Set, J. Math. Anal. and Applications, 205(1997)531-536.

*19. (with Wang Hui) A Minimization Problem Arising from Prescribing Scalar Cur- vature Functions, Math. Z. 222(1996)1-6.

*18. A Result on the Kazdan-Warner Problem. Bull. Sc. Math. France, 119(1995)409- 418.

*17. The Yamabe Problem with Dirichlet Data, C.R.Acad.Sci. Paris, t320, Serie I,P709- 712, 1995.

16. Conformal Deformations on a Two Dimensional Open Manifolds with Prescribed Gaussian Curvature, Tsinghua University Press, 1995.

15. The Dirichlet Problem at Infinity on a Quasi-hyperbolic manifold, P195-207, ed. K.S.Chang and K.C.Chang, South Korea Press, 1995.

14. (with Chang Xiaodong and Lu Qiang) A Remark on Local Decomposition of Non- linear Control Systems, Proceeding of Applied and Industry Math., Tsinghua University Press, (1994) P711-714.

*13. Conformal Deformations on a Non-compact Riemannian Manifold, Math. Ann. Vol. 295(1993)63-69.

12. Regularity of Minimizing Harmonic Maps into Ellipsoids, Acta Math. Sinica, (New Series) 9(1)(1993) 63-69.

11. Minimal Graph Evolutions in the Hyperbolic Space, in a Collected Papers of the First Conference of Chinese Postdoctors, Academic Press, 1993.

10. A Perturbation Result for Superlinear Klein-Gordon Equations, In a symposium on Nonlinear Problems in Sciences and Engineering, Academic Press, 1992.

*9. Harmonic Map Heat Flow with Free Boundary, Comment. Math. Helv. 66(1991)279- 301.

8. Positive Solutions of the Yamabe Equation on Complete Non-compact Riemannian Manifolds, A Collected Papers of Chinese Postdoctors (4), Peking University Press, 1991.

*7. On Equivariant Harmonic Maps Defined on a Lorentz Manifold, Ann. Inst. Fourier, 42(1991)511-518.

6. On Non-linear Eigen-problems of Quasilinear Elliptic Operators, J. Partial Diff. Equations, 493(1991)56-72.

5. Some Notes about Positive Solutions of a Semilinear Elliptic pde with Sobolev Exponent, Acta Math. Sinica, (New Series) 7(4)(1991)342-347.

*4. On Equivariant Harmonic Maps into a Lorentz Manifold, C.R.Acad. Sci. Paris, t311, Serie I, P439-422, 1990.

3. New Examples of Harmonic Map Heat Flow in Dimension Two, in a Collected Papers of Chinese Postdoctors(3), Academic Press, 1990.

2. A Nontrivial Solution of a Semilinear Elliptic Partial Diff. Equations, in a collected papers of Department of Applied Math., Tsinghua University. 1991.

1. Harmonic Maps with Prescribed Finite Singularities, Ph.D. Thesis, Academic Sinica, Beijing, 1989.

Preprints: 4, Li Ma, J.Bland, When is the Hawking Mass monotone under geometric flows, arxiv.org.

3. Conformal Metrics with Prescribed Mean Curvature on the Boundary of the Unit

Ball, Rutgers Univ., 1996.

2. (with A.Bahri and Y.Chen) Multiplicity results of the Scalar Curvature Problems on the Sphere of Dimensions 3 and 4.

1. Bifurcation in the Scalar Curvature Problems, Preprint, Rutgers University, 1996.