姓   名：关庄丹

职   称：教 授

办公室：F206

邮   箱： guan@henu.edu.cn

网站主页：https://math.ucr.edu/~zguan/bib.html

研究方向：复几何和微分几何，齐性空间

教育背景：

1990.09-1993.06， 博士， 加州大学伯克来分校， 基础数学专业

1983.09-1986.06， 硕士， 中国科学院数学所， 基础数学专业

1978.10-1982.06， 学士， 厦门大学， 基础数学专业

工作经历：

2019.01至今， 河南大学， 教授

2018.09-2018.12 河南大学， 访问教授

2004.07-2018.11，加州大学， 副教授

2000.07-2004.07, 加州大学， 助理教授

1993.07-2000.06，普林斯顿大学， 助理教授及副教授

代表性论文：

• 1. Examples of Holomorphic Symplectic Manifolds which admit no K\"ahler Structure II, Invent. Math. vol. 121(1995), 135-145. (see also F. Bogomolov: On Guan's Examples of Simply Connected Non-K\"ahler Compact Complex Manifolds, Amer. J. Math. 118(1996), 1037-1046). MR 97i:32033.

• 2. On the Betti Numbers of Irreducible Compact Hyperk\"ahler Manifolds of Complex Dimension Four, Math. Res. Letters vol 8 (2001), 663--669.

• 3. Some Applications of Group Actions in Complex Geometry, Chin. Quart. J. Math. 38 (2023), 254--275. doi: 10.13371/j.cnki.chin.q.j.m.2023.03.002 MR 4770654

• 4. (with J. Chen)Generalized Maxwell-Einstein Metrics on Certain CP^1 bundles, 20 pages, accepted and to appear in Acta Mathematica Scientia 2025

• 5. Maxwell-Einstein Metrics on Completions of Certain C* Bundles, Acta Mathematica Scientia 43B(2023), p. 363---372. doi: 10.1007/s10473-023-0120-9. MR 4498386

• 6. On Some Recent Progress in Complex Geometry---the Area Related to Homogeneous Manifolds, Chinese Quart. J. of Math. 35(2020), p. 111--144. doi: 10.13371/j.cnki.chin.q.j.m.2020.02.001. See also 1 and 2 MR 4756779

  论文：

  1.(with M. X. Liang)Complete Co-homogeneity One Kahler Metrics on the Affine Quadric of Complex Dimension Two(related to a Cohomogeneity One Point of View of A Yau Conjecture)II---New Hyperkahler Metrics, in preprint 2024, 47 pages and submitted

• (with N. Li, Z. Wang)Some remarks on existence of a complex structure on the compact six sphere, in preprint 2024, 15 pages, accepted and to appear in Axioms

• (with J. Chen, Y. Y. Tang)The calculations of holomorphic bisectional curvatures of a co-homogeneity one K\"ahler metric on type III domains, in preprint 2023, 12 pages and submitted

• (with J. Chen, S. J. Jing, Y. Y. Tang)The Extremal Metric on A Class of Twisted Fock-Bargmann-Hartog Domains, 10 pages, in preprint 2023 and submitted

• 2. Some Applications of Group Actions in Complex Geometry, Chin. Quart. J. Math. 38 (2023), 254--275. doi: 10.13371/j.cnki.chin.q.j.m.2023.03.002 MR 4770654

• 3. (with M. X. Liang)Complete Co-homogeneity One Kahler Metrics on the Affine Quadric of Complex Dimension Two(related to a Cohomogeneity One Point of View of A Yau Conjecture), Chin. Quart. J. Math. 39 (2024), 200--220. doi: 10.13371/j.cnki.chin.q.j.m.2024.02.008

• (with J. Chen)Generalized Maxwell-Einstein Metrics on Completions of Certain C* Bundles, in preparation

• 4. (with J. Chen)Generalized Maxwell-Einstein Metrics on Certain CP^1 bundles, 20 pages, accepted and to appear in Acta Mathematica Scientia 2025

• 5. (with M. X. Liang)Complete Kahler Metrics with Positive Holomorphic Sectional Curvatures on Certain Line Bundles(related to a Cohomogeneity One Point of View of A Yau Conjecture)--II, 16 pages, accepted and to appear in Acta Mathematica Sinica

• 6. (with X. M. Duan)Complete Kahler Metrics with Positive Holomorphic Sectional Curvatures on Certain Line Bundles(relatd to a Cohomogeneity One Point of View of A Yau Conjecture), Acta. Math. Scientia, vol. 44B (2024), pp.78--102. doi: 10.1007/s10473-024-0103-5.

• 7. Maxwell-Einstein Metrics on Completions of Certain C* Bundles, Acta Mathematica Scientia 43B(2023), p. 363---372. doi: 10.1007/s10473-023-0120-9. MR 4498386

• 8. (with Z. H. Wang)A Note on the Nonexistence of A Complex Threefold As A Conjugate Orbit of G2, Results in Math. 77(2022), Article 139. doi: 10.1007/s00025-022-01678-5.

• 9. On Some Recent Progress in Complex Geometry---the Area Related to Homogeneous Manifolds, Chinese Quart. J. of Math. 35(2020), p. 111--144. doi: 10.13371/j.cnki.chin.q.j.m.2020.02.001. See also 1 and 2 MR 4756779

• 10. Type II Compact Almost Homogeneous Manifolds of Cohomogeneity One---II, Intern. J. Math. 30(2019), No. 13, Article 1940002. doi: 10.1142/S129167X19400020. IJM10

• 11. Nonexistence of S^6 type Threefolds, Pacific J. of Math. 305(2020), p. 641--644.doi: 10.2140/pjm.2020.305.641

• 12. (with P. Orellana and A. Van) Type I Compact Almost Homogeneos Manifolds of Cohomogeneity One---IV Axioms 8(2019), no. 1, art. 2.

• 13. A New Proof of A Conjecture on Nonpositive Ricci Curved K\"ahler-Einstein Surfaces Mathematics 6(2018), no. 2, art. 21. doi: 10.3390/math6020021.

• 14. A Classification of Compact Cohomogeneity One Locally Conformal K\"ahler Manifolds, Mathematics 12(2024), no. 11, art. 1710. doi: 10.3390/math12111710.

• 15. A Note on the Classification of Compact Complex Homogeneous Locally Conformal K\"ahler Manifolds Journal of Mathematics and Statistics 13(2017), no. 3. p. 261--267. doi: 10.3844/jmssp.2017.261.267.

• Examples of Simply Connected Holomorphic Symplectic Manifolds which are not Formal I, in preprint 2015; 13 pages.

• 16. (with P. Cernea) Killing Fields Generated by Multiple Solutions to the Fischer-Marsden Equation Intern. J. Math. 26 (2015), no. 4. doi: 10.1142/S0129167X15400066. IJM9

• 17. (with P. Cernea) Killing Fields Generated by Multiple Solutions to the Fischer-Marsden Equation II Intern. J. Math. 27 (2016), no. 10. doi: 10.1142/S0129167X16500804. IJM8

• Modification and the Cohomology Groups of Compact Solvmanifolds II, in preprint and submitted 2013

• Classification of Real Eight Dimensional Compact Solvmanifolds with Real Symplectic Structures, in preparation 2013

• m-extremal metrics and m-Calabi flows, in preparation 2012.

• 18. On Bisectional Negatively Curved Compact K\"ahler-Einstein Surfaces, Pacific Journal of Mathematics 288 (2017), 343--353.

• 19. Positive Lemma, Generalized Extremal-solitons and Second Order Linear Differential Equations, Advancement and Development in Mathematical Science, vol 1 (2012), issue 2, 13--32.

• 20. Toward a classification of compact real solvmanifolds with real symplectic structures, Journal of Algebra 379 (2013), 144--155. doi: 10.1016/j.algebra.2013.01.011.

• 21. On Classification of Compact Complex Solvmanifolds, doi: 10.1016/j.jalgebra.2011.08.026, J. of Algebra, vol 347 (2011), 69--82.

• 22. Toward a Classification of Symplectic Nilmanifolds, International Mathematical Research Notices, vol 2010 (2010), 4377--4384 2010:doi:10.1093/imrn/rnq049.

• 23. Affine Compact Almost-Homogeneous Manifolds of Cohomogeneity One Central European Journal of Mathematics, vol 7 (2009), 84--123. Note: Theorem 10.2 is true when the manifold is Fano, cohomogeneity one and has a semisimple automorphism group. doi:10.2478/s11533-008-0055-3

• 24. Classification of Compact Complex Homogeneous Manifolds with Pseudo-k\"ahlerian Structures, Jour. of Algebra, vol 324 (2010), 2010--2024; doi:10.1016/j.jalgebra.2010.06.013

• 25. Classification of Compact Homogeneous Manifolds with Pseudo-k\"ahlerian Structures (Announcement) Comptes Rendus Math\'ematiques de l'Acad. Sci. Canada, vol 31 (2009), no. 1. 20--23.

• 26. Modification and the Cohomology Groups of Compact Solvmanifolds, ERA-AMS 13 (2007), 74--81; see also Comments

• A Complete Classification of Compact Almost Homogeneous K\"ahler Manifolds of Cohomogeneity One with a Higher Codimensional End, in preparation.

• 27. Type I Compact Almost Homogeneous Manifolds of Cohomogeneity One---I, Pacific J. of Appl. Math., vol 3 (2011), 43--72(Original proof Jan. 20, 2011).

• 28. Type I Compact Almost Homogeneous Manifolds of Cohomogeneity One---II, Pacific J. of Appl. Math., vol 3 (2011), 179--202(Original proof Jan. 21, 2011).

• 29. Type I Compact Almost Homogeneous Manifolds of Cohomogeneity One---III, Pacific J. of Mathematics, vol. 261 (2013), 369--388; doi:10.2140/pjm.2013.261.369.

• 30. Type II Compact Almost Homogeneous Manifolds of Cohomogeneity One, Pacific J. of Mathematics, vol. 253 (2011), 383--422; doi:10.2140/pjm.2011.253.383.

• 31. Moser Vector Fields and Geometry of the Mabuchi Moduli Space of K\"ahler Metrics, Geometry, 2014 (2014), article 968064.

• Jacobi Fields and the Geodesic Stability, in preparation.

• Book cooperated with S. Kobayashi: Compact Complex Manifolds and K\"ahler Geometry, in process.

• Testing the Geodesic Stability on Toric Bundles, in preparation.

• 32. Extremal-Solitons and Exponential C^{\infty} Convergence of Modified Calabi Flow on Certain CP^1 bundles, Pacific J. Math. vol. 233 (2007), 91-124; doi:10.2140/pjm.2007.233.91.

• 33. Existence of Extremal Metrics on Almost Homogeneous Manifolds of Cohomogeneity One---IV, Ann. Glob. Anal. Geom. 30(2006), 139--167.

• An Inequality of Rozansky-Witten Invariants, in preparation.

• 34. On Representation Theory and the Cohomology Rings of Irreducible Compact Hyperk\"ahler Manifolds of Complex Dimension Four, Central European Journal of Mathematics, vol 1 (2003), 661--669. See also original tex file

• 35. On the Betti Numbers of Irreducible Compact Hyperk\"ahler Manifolds of Complex Dimension Four, Math. Res. Letters vol 8 (2001), 663--669.

• 36. On Modified Mabuchi Functional and Mabuchi Moduli Spaces of K\"ahler Metrics on Toric Bundles. Math. Research Letters vol 6 (1999), 547--555.

• Quasi-Einstein Metrics and Evolution of Metrics in a K\"ahler Class, a preprint will come out soon.

• 37. (with X. Chen) Existence of Extremal Metrics on Almost Homogeneous Manifolds of Cohomogeneity One, Asian J. Math. vol 4 (2000), 817--830..

• 38. Existence of Extremal Metrics on Almost Homogeneous Manifolds of Cohomogeneity One---II, Journal of Geometric Analysis, vol 12 (2002), 63--79. The final version before publication

• 39. Existence of Extremal Metrics on Almost Homogeneous Manifolds of Cohomogeneity One---III, International Journal of Mathematics, vol 14 (2003), 259--287. The final version before publication IJM7

• 40. Toward a Classification of Compact Complex Homogeneous Manifolds, Journal of Algebra vol. 273 (2004), 33--59; doi:10.1016/j.jalgebra.2003.11.007.

• Toward a Classification of Compact Complex Homogeneous Manifolds II, in preparation.

• 41. On Compact Symplectic Manifolds with Lie Group Symmetries, Transactions of AMS. 357 (2005), 3359-3373.

• Classification of Compact Contact Homogeneous Spaces, a preprint will come out soon.

• 42. Classification of Compact Complex Homogeneous Spaces with Invariant Volumes, Transactions of AMS. 354(2002) 4493-4504. 42' Announcement appeared in ERA-AMS vol 3 (1997), 90-92.

• 43. Classification of Compact Homogeneous Spaces with Invariant Symplectic Structures, ERA-AMS vol 3 (1997), 52-54.

• 44. Toward a Classification of Almost Homogeneous Manifolds II---Bad Models, International J. Math., vol 10 (1999), 571--586. IJM6

• 45. Toward a Classification of Almost Homogeneous Manifolds III---SL(2)xC* Actions, International J. Math., vol 11 (2000), 799--809. IJM5

• 46. A Splitting Theorem for Compact Complex Homogeneous Space with a Symplectic Structure, Geometrica Dedicata vol. 63(1996), 217-225. MR 98a:53105.

• 47. Examples of Holomorphic Symplectic Manifolds which admit no K\"ahler Structure II, Invent. Math. vol. 121(1995), 135-145. (see also F. Bogomolov: On Guan's Examples of Simply Connected Non-K\"ahler Compact Complex Manifolds, Amer. J. Math. 118(1996), 1037-1046). MR 97i:32033.

• 48. Examples of Holomorphic Symplectic Manifolds which admit no K\"ahler Structure III, International J. of Math. vol. 6(1995), 709-718. MR 97i:32034. IJM4

• 49. Examples of Compact Holomorphic Symplectic Manifolds Which Are Not K\"ahlerian, (In Geometry and Analysis on Complex Manifolds---Festschift for Professor S. Kobayashi's 60-th birthday, World Scientific Publishing Co. 1994), 63-74.

• 50. Existence of Extremal Metrics on Almost Homogeneous Spaces with Two Ends. Transaction of AMS, vol. 347(1995), 2255-2262.

• 51. Quasi-Einstein Metrics, International J. of Math., vol. 6(1995), 371-379. MR 96e:53060. IJM3

• 52. Stablity of Hermitian Vector Bundles, a Quantitative Point of View, Intern'l J. Math. 3 (1992), 477-481. MR 93k:32067. IJM2

• 53. Toward a Classification of Almost Homogeneous Manifolds I---Linearization of the Singular Extremal Rays. International J. of Math., vol 8(1997), 999-1014. IJM1

• 54. (with Dorfmeister) Fine Structures of Reductive Pseudo-K\"ahlerian Spaces, Geometrica Dedicata 39 (1991), 321-338. MR 92h:53081. 54' Supplement in Geom. Dedi. 42 (1992), 241-242.

• 55. (with Dorfmeister) Pseudo-K\"ahlerian Homogeneous Spaces Admitting a Reductive Transitive Group of Automorphisms, Math. Zeitschrift 209 (1992), 89-100. MR 92k:32058.

• 56. (with Dorfmeister) Classification of Compact Homogeneous Pseudo-K\"ahler Manifolds, Comm. Math. Helv. 67 (1992), 499-513. MR 93i:32042.(see also Huckleberry A. L.: Homogeneous Pseudo-K\"ahlerian Manifolds: A Hamiltonian Viewpoint, Note di Matematica 10(1990) suppl. 2. 337-342. MR 94f:53052).

• 57. (with Y. Hong and H. C. Yang) A Remark on K\"ahler-Einstein Manifolds, Acta Math. Sinica 31 (1988), 595--602. MR 0983430 (90c:53171).

• 58. Curvature on the Hermitian Symmetric Spaces. Acta Math. Sinica. New Series 4 (1988), 270-283.

科研项目：

1. 项目名称（编号），美国国家科学基金项目，2001/07-2005/08，已结题，主持；

2. 项目名称:一些特殊的复几何结构理论及多复变函数论,编号:12171140，国家自然科学基金面上项目，2022/01-2025/12，51万元，主持。

3. 项目名称（编号），美国国家科学基金项目，1994/07-1997/08，已结题，副主持；

4. 项目名称（编号），美国国家科学基金项目（NSF Fellowship)，1996/07-1999/12， 已结题， 主持；

主讲课程：

24年秋：黎曼几何；23年秋：黎曼曲面；22年秋：流形上的分析；22年春：复几何；21年秋：代数几何

学术交流：

1. 2021年08月受邀在全国多复变大会做关于广义Maxwell-Einstein度量的报告；

2. 2021年07月受邀在厦门大学做关于实六维球面上复结构的报告；等等

荣誉与奖励:

1996年 获NSF Fellowship奖项

1989年 获优秀博士生Fellowship奖

Name：Guan, Zhuang-dan Daniel

Title：Prof. Dr.

Office：F206

Email： guan@henu.edu.cn

Research Field：Complex Geometry, Differential Geometry and Homogeneous Spaces

Education：

1990.09-1993.06, Ph.D.， University of California at Berkeley

1983.09-1986.06, Master of Science, Institute of Mathematics, Academic Sininca, Beijing, China

1978.10-1982.06, Bachelor of Science, Xiamen University, Xiamen, China

Position：

2019.01-， Henan University，Professor

2004.07-2018.11, University of California at Riverside, Associate professor

2018.09-2018.12, Henan University, Visiting Professor

1993.09-2004.07, Princeton University and University of California at Riverside, Assistant professor

Selected publications：

[1]D. Guan, Examples of compact holomorphic symplectic manifolds which are not

Kählerian II, Invent Math. 121 (1995), 135-145.

[2]D. Guan, On the Betti Numbers of Irreducible Compact Hyperkähler Manifolds of Complex Dimension Four, Mathematical Research Letters 8 (2001), 663-669.

Research Funding：

1. D. Guan，National Natural Science Foundation of USA(XXX)，2001.07-2005.08, PI

2. D. Guan, National Natural Science Foundation of China

3. D. Guan，National Natural Science Foundation of USA(XXX)，1994.07-1997.08, CPI(PI: Hsiang, W. C.).

4. D. Guan，National Natural Science Foundation of USA(XXX, NSF Fellow)，1996.07-1999.12, PI.

Teaching：

Algebraic Geometry, Fall 2021；Riemanian Geometry, Fall 2024; Complex Geometry, Spring 2022; etc.

Talks：

1. 2021.07, Xiamen University；

2. National Several Complex Variable Conference 2023; etc.

Honor and awards

Excellent Fellowship, NSF Fellowship