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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Recent progress on holomorphic Morse inequalities
全纯 Morse不等式 CR流形
2023/11/13
In this talk, we present recent progress on holomorphic Morse inequalities. We first review the history and motivation. Then we introduce recent results on CR manifolds. Finally we give a uniform proo...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Bergman reproducing kernels for nearly holomorphic functions on bounded symmetric domains
伯格曼 有界对称域 近乎全纯函数 核
2023/4/17
Nearly holomorphic functions on symmetric domains are defined by Shimura as polynomial of differential of Kaehler potential with holomorphic coefficients. We find the corresponding Bergman reproducing...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Bergman reproducing kernels for nearly holomorphic functions on bounded symmetric domains
伯格曼 有界对称域 近乎全纯函数 核
2023/4/23
Nearly holomorphic functions on symmetric domains are defined by Shimura as polynomial of differential of Kaehler potential with holomorphic coefficients. We find the corresponding Bergman reproducing...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Lines on holomorphic contact manifolds and a generalization of (2,3,5)-distributions to higher dimensions
全纯接触流形 线和 （2，3，5） 高维度推广
2023/4/19
Since the celebrated work by Cartan, distributions with small growth vector (2,3,5) have been studied extensively. In the holomorphic setting, there is a natural correspondence between holomorphic (2,...
Optimal Recovery of Holomorphic Functions from Inaccurate Information about Radial Integration
Approximation Optimal Recovery Holomorphic
2013/1/30
This paper addresses the optimal recovery of functions from Hilbert spaces of functions on the unit disc. The estimation, or recovery, is performed from inaccurate information given by integration alo...
The theory of Hahn meromorphic functions, a holomorphic Fredholm theorem and its applications
Hahn meromorphic functions holomorphic Fredholm theorem its applications Classical Analysis and ODEs
2012/5/9
We introduce a class of functions near zero on the logarithmic cover of the complex plane that have convergent expansions into generalized power series. These power series are general enough to cover ...
Non-holomorphic projections and extension of biholomorphic mappings
Non-holomorphic projections extension of biholomorphic mappings Complex Variables
2012/5/24
We show that biholomorphic mappings between two bounded, pseudoconvex domains with smooth boundary extend smoothly to the boundaries of the domains, under a regularity condition on a family of twisted...
Large Harnack inequalities, Kobayashi distances and holomorphic motions
Large Harnack inequalities Kobayashi distances holomorphic motions Complex Variables
2012/4/18
We prove some generalizations and analogies of Harnack inequalities for pluriharmonic, holomorphic and "almost holomorphic" functions. The results are applied to the proving of smoothness properties o...
Condition R and proper holomorphic maps between equidimensional product domains
Condition R proper holomorphic maps equidimensional product domains Complex Variables
2012/4/17
We consider proper holomorphic mappings of equidimensional pseudoconvex domains in complex Euclidean space, where both source and target can be represented as Cartesian products of smoothly bounded do...
On the existence of stable compact leaves for transversely holomorphic foliations
Holomorphic foliation holonomy stable leaf
2012/4/17
A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.
On Kazhdan's Property (T) for the special linear group of holomorphic functions
Kazhdan's Property (T) special linear group holomorphic functions
2012/3/1
We investigate when the group $SL_n(\mathcal{O}(X))$ of holomorphic maps from a Stein space $X$ to $SL_n (\C)$ has Kazhdan's property (T) for $n\ge 3$. This provides a new class of examples of non-loc...
Stein neighborhoods of graphs of holomorphic mappings
Plurisubharmonic functions pluripotential theory
2011/9/20
Abstract: In this paper we provide sufficient conditions for the graphs of holomorphic mappings on compact sets in complex manifolds to have Stein neighborhoods. We show that under these conditions th...
Open problems in local discrete holomorphic dynamics
local discrete holomorphic dynamics Dynamical Systems
2011/9/20
Abstract: This paper contains a selection, dictated by personal taste and by no means complete, of open problems in local discrete holomorphic dynamics.
On the number of factors in the unipotent factorization of holomorphic mappings into $\text{SL}_2(\mathbb{C})$
number of factors unipotent factorization of holomorphic $\text{SL}_2(\mathbb{C})$
2011/1/18
We estimate the number of unipotent elements needed to factor a null-homotopic holomorphic map from a finite dimensional reduced Stein spaces X into SL2(C) .
We classify compact K\"ahler manifolds $M$ of dimension $n\geq 3$ on which acts a lattice of an almost simple real Lie group of rank $\geq n-1$. This provides a new line in the so-called Zimmer progr...