On the upper semicontinuity of the Wu metric

Upper semicontinuity of the dimensions of automorphism groups of domains in $C^n$

Let $H^n$ be the metric space of all bounded domains in $C^n$ with the metric equal to the Hausdorff distance between boundaries of domains. We prove that the dimension of the group of automorphisms of domains is an upper semicontinuous function on $\H^n$. We also provide theorems and examples regarding the change in topological structure of these groups under small perturbation of a domain in $H^n$.

On the Wu metric in unbounded domains

We discuss the properties of the Wu pseudometric and present counterexamples for its upper semicontinuity that answers the question posed by Jarnicki and Pflug. We also give formulae for the Wu pseudometric in elementary Reinhardt domains.

代数维数的上半连续性

Upper semicontinuity of algebraic dimension

本文证明Moishezon流形在光滑形变下极限仍为Moishezon，并推广到满足∂∂̄-引理的浸没，通过Barlet循环空间与Rao-Tsai无挠方法及相位估计，确立代数维数的上半连续性。

Upper bounds for Bergman kernels associated to positive line bundles with smooth Hermitian metrics

Off-diagonal upper bounds are established away from the diagonal for the Bergman kernels associated to high powers of holomorphic line bundles over compact complex manifolds, asymptotically as the power tends to infinity. The line bundle is assumed to be equipped with a Hermitian metric with positive curvature form, which is infinitely differentiable but not necessarily real analytic. The bounds obtained are the best possible for this class of metrics.