会议题目：2021年河南大学复分析与复几何研讨会议

腾 讯 ID：156557374

会议安排：

 

时间			主持人	报告人	题目
8 月 23 日	上午	8:00-8:10	冯淑霞	开幕式
		8:10-9:00	刘太顺	曹廷彬	Value distribution of difference operators in several complex variables and complex delay PDE
		9:00-9:50		谢松晏	On Ahlfors currents
		休息
		10:10-11:00	王安	于光升	A second main theorem of Nevanlinna theory for moving targets
		11:00-11:50		张硕	A study of the properties of the Bergman projections on generalized Hartogs triangles
	下午	14:30-15:20	吴可	邵国宽	Equidistribution theorems on strongly pseudoconvex CR manifolds
		15:20-16:10		李小山	S1-equivariant Index theorems and Morse inequalities on complex manifolds with boundary
		休息
		16:30-17:20	周泽华	李军	Early history of pluripotential theory
		17:20-18:10		宁家福	The extension of quasi-plurisubharmonic functions on compact Kähler manifolds
8 月 24 日	上午	8:00-8:50	邱春晖	苏桂聪	Kobayashi isometry on the symmetrized bidisc
		8:50-9:40		谭举	Left-invariant conformal vector fields on non-solvable Lie groups
		休息
		10:00-10:50	涂振汉	何玲	Minimal surfaces in Quaternionic projective spaces
		10:50-11:40		毕恩超	The Kobayashi pseudometric for some Hartogs domains
	下午	14:30-15:20	乔玉英	李鸿军	Holomorphic Automorphism Groups of (m,1)-Circular Domains
		15:20-16:10		吕小芬	Doubling Fock spaces and related operators
		休息
		16:30-17:20	刘浩	唐言言	Special Toeplitz operators on a class of bounded Hartogs domains
		17:20-18:10		吴菊杰	A counter example for the uniform Mergelyan approximation in C2

   

摘 要：

Value distribution of difference operators inseveral complex variables

and complex delay PDE

曹廷彬（南昌大学）

In this talk, I mainly introduce the recent development of the value distribution theory for difference operators inseveral complex variables, and its applications into complex delay partial differential equations.

On Ahlfors currents

谢松晏（中国科学院数学与系统科学研究院）

We answer a basic question in Nevanlinna theory that Ahlfors currents associated to thesame entire curve may be nonunique. Indeed,we will construct one exotic entire curve whichproduces infinitely many cohomologically different Ahlfors currents. Moreover, concerningSiu's decomposition, for an arbitrary positiveinteger k or k=infinity, some of the obtained Ahlfors currents have singular parts supported onk irreducible curves. In addition, they can havenonzero diffuse parts as well, which answers aquestion of Brunella.This is joint work with DinhTuan Huynh (arxiv.org/abs/2101.11973，JMPA2021).

A second main theorem of Nevanlinna theory for moving targets

于光升（宁波大学）

We will give a second main theorem for nonconstant holomorphic curves with moving targets, which removes the algebracially nondegenerate assumption in previous results. This result can be regarded as a generalization of Cartan's conjecture for moving hypersurfaces. We will also consider the corresponding Schmidt subspace theorem result in Diophantine approximation.

A study of the properties of the Bergman projections on generalized Hartogs triangles

张硕（天津理工大学）

In this talk, we study the boundedness for the Bergman projections of some generalized Hartogs triangles on L^p and L^p Sobolev spaces. We also obtain the L^p-norm estimates for the Bergman projections on some generalized Hartogs triangles.

Equidistribution theorems on strongly pseudoconvex CR manifolds

邵国宽（中山大学）

The study of equidistribution of zeros of holomorphic sections has become intensively active in recent years. In this talk, we discuss equidistribution theorems on zeros of CR functions on a strongly pseudoconvex CR manifoldXwith an S1-action. One of the main ingredients in the proof is a uniform estimate of the Szego kernel onX. This is a joint work with Chin-Yu Hsiao.

S1-equivariant Index theorems and Morse inequalities on

complex manifolds with boundary

李小山（武汉大学）

Early history of pluripotential theory

李军（湖南大学）

In this talk I will review early works on pluripotential theory and its applications. Based on published papers before 1990, I will recall some important problems in pluripotential theory. The main focus will be the background, the motivation and main ideas around theses problems.

The extension of quasi-plurisubharmonic functions on compact Kähler manifolds

宁家福（中南大学）

In this talk, I will report some recent results about the extension of (quasi-)plurisubharmonic functions on (compact Kähler) manifolds. I’ll also introduce the extension when the submanifold has holomorphic retraction structure, which is the case of a joint work with Prof. Zhiwei Wang and Prof. Xiangyu Zhou.

Kobayashi isometry on the symmetrized bidisc

苏桂聪（雅盖隆大学）

Kobayashi isometry is the question of considering the complex structure of the Kobayashi hyperbolic manifold M determined by the Kobayashi metric k_M. In this talk, we will introduce some basic conclusion and proof of Kobayashi isometry in the strictly convex domain. And then we will give a similar result on the symmetrized bidisc.

Left-invariant conformal vector fields on non-solvable Lie groups

谭举 (安徽工业大学)

Minimal surfaces in Quaternionic projective spaces

何玲（天津大学）

The Kobayashi pseudometric for some Hartogs domains

毕恩超（青岛大学）

The study of Kobayashi pseudometric is one of the classical topic in complex analysis and complex geometry. In general, it is difficult to obtain the explicit expression of the Kobayashi pseudometric. In this talk, we will give the specific forms of geodesics for some Hartogs domain in the sense ofKobayashi pseudometric. Then by using the formula of geodesics, we determine the Kobayashi pseudometric for the F-B-H type domains.

Holomorphic Automorphism Groups of (m,1)-Circular Domains

李鸿军 (河南大学)

Doubling Fock spaces and related operators

吕小芬（湖州师范学院）

In this talk, we will discuss the Carleson measures for doubling Fock spaces and obtain the characterizations on Toeplitz and Hankel operators based on the pointwise estimates for Bergman kernel. We also get the estimates on Bergman kernel for Bergman spaces with exponential weights.

Special Toeplitz operators on a class of bounded Hartogs domains

唐言言（河南大学）

We introduce a wide class of bounded Hartogs domains in Cn, which contains some generalizations of the classical Hartogs triangle. A sharp criterion for the Lp-Lq boundedness of the Toeplitz operator with the symbol K-t is obtained on these domains, where K is the Bergman kernel on the diagonal and t≥0. It generalizes the results by Beberok and Chen in the case 1<p<+∞. This is a joint work with Tu Zhenhan.

A counter example for the uniform Mergelyan approximation in C2

吴菊杰（中山大学）