Intrinsic derivative, curvature estimates and squeezing function
Intrinsic derivative, curvature estimates and squeezing function
复制标题
固有导数、曲率估计和挤压函数
DOI：
10.1007/s11425-016-9043-8
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发表时间：
2017
影响因子：
1.4
通讯作者：
Zhang LiYou
中科院分区：
文献类型：
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作者：
Zhang LiYou
这份调查报告分为两部分。首先，我们回顾了Lu（1979）引入的内禀导数的概念以及他在最近十年中所做的相关工作，包括无穷维Grassmann流形的全纯等距嵌入和有界域的Bergman曲率估计.受Lu思想的启发，我们给出了Bergman曲率的上下界估计，这是由Deng et al.（2012）最初引入的压缩函数概念。最后，我们回顾了严格伪凸边界点附近Bergman曲率的渐近行为的一些最新进展，并提出了关于n中有界域的压缩函数的一些公开问题。
This survey paper consists of two folds. First of all, we recall the concept of intrinsic derivative which was introduced by Lu (1979) and the related works due to Lu in his last ten years, including the holomorphically isometric embedding into the infinite dimensional Grassmann manifold and the Bergman curvature estimates for bounded domains in ℂn. Inspired by Lu’s idea, we give the lower and upper bounds estimates for the Bergman curvatures in terms of the squeezing function—one concept originally introduced by Deng et al. (2012). Finally, we survey some recent progress on the asymptotic behaviors for Bergman curvatures near the strictly pseudoconvex boundary points and present some open problems on the squeezing functions of bounded domains in ℂn.