Characterizing strong pseudoconvexity, obstructions to biholomorphisms, and Lyapunov exponents
Characterizing strong pseudoconvexity, obstructions to biholomorphisms, and Lyapunov exponents
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DOI：
10.1007/s00208-018-1715-7
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发表时间：
2017-03
影响因子：
1.4
通讯作者：
Andrew M. Zimmer
中科院分区：
文献类型：
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作者：
Andrew M. Zimmer
本文考虑了如下问题：对于边界光滑的有界域，强伪凸性能否用域的内在复几何来刻画？我们的方法来回答这个问题是基于理解的动力学行为的真实的测地线的小林度量，并允许我们证明了一些结果的域低的正则性。例如，我们证明了对于具有边界的凸域，强伪凸性可以用边界附近的压缩函数的行为，边界附近Bergman度量的全纯截面曲率的行为，或者边界附近的复几何的任何其他合理的度量来刻画.第一个特征给出了一个问题的部分答案Fornæss和沃尔德。作为这些刻画的应用，我们证明了一个有边界的凸域如果双全纯于一个强伪凸域，那么它也是强伪凸的。
In this paper we consider the following question: For bounded domains with smooth boundary, can strong pseudoconvexity be characterized in terms of the intrinsic complex geometry of the domain? Our approach to answering this question is based on understanding the dynamical behavior of real geodesics in the Kobayashi metric and allows us to prove a number of results for domains with low regularity. For instance, we show that for convex domains withboundary strong pseudoconvexity can be characterized in terms of the behavior of the squeezing function near the boundary, the behavior of the holomorphic sectional curvature of the Bergman metric near the boundary, or any other reasonable measure of the complex geometry near the boundary. The first characterization gives a partial answer to a question of Fornæss and Wold. As an application of these characterizations, we show that a convex domain withboundary which is biholomorphic to a strongly pseudoconvex domain is also strongly pseudoconvex.