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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...
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...
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...
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,...
Perhaps the most useful analytic tool in gauge theory is the Uhlenbeck compactness theoremfor sequences of unitary connections on hermitian vector bundles [U]. Given connections {Dj} ona bundle E over...
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...
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 ...
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...
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...
We present a general formula for the Gaussian curvature of curved holomorphic 2-spheres in Grassmannian manifolds G(m, n). We then show how to construct such solutions with constant curvature. We also...
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...
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.
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...
Abstract: We develop an Hamiltonian representation of the sl(2,C) algebra on a phase space consisting of N copies of twistors, or bi-spinors. We identify a complete set of global invariants, and show ...
Stein neighborhoods of graphs of holomorphic mappings     Plurisubharmonic functions  pluripotential theory       font style='font-size:12px;'> 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...

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