Geometry of domains with the uniform squeezing property

By Sai-Kee Yeung. 2009

121 citations recorded by the source corpus.

Abstract We introduce the notion of domains with uniform squeezing property, study various analytic and geometric properties of such domains and show that they cover many interesting examples, including Teichmuller spaces and Hermitian symmetric spaces of non-compact type. The properties supported by such manifolds include pseudoconvexity, hyperconvexity, Kahler-hyperbolicity, vanishing of cohomology groups and quasi-isometry of various invariant metrics. It also leads to nice geometric properties for manifolds covered by bounded domains and a simple criterion to provide positive examples to a problem of Serre about Stein properties of holomorphic fiber bundles.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5ed6f9ce1a9bda40fcb51413eb2daa398d0dd38e

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In Applied Mathematics

1. Kang-Tae Kim
2. Liyou Zhang
3. Qi’an Guan
4. F. Deng
5. Xiangyu Zhou
6. B. Berndtsson

In Geometry and Topology

1. Kang-Tae Kim
2. Liyou Zhang
3. Qi’an Guan
4. F. Deng
5. Xiangyu Zhou
6. B. Berndtsson

Citations in the corpus

• On the uniform squeezing property of bounded convex domains in ℂn (2016, methodology): “Not only does this theorem cover the case left untreated in [Yeung 2009], but our method is different (see also [Deng et al.”
• Some properties of squeezing functions on bounded domains (2011, background): “Holomorphic homogeneous regular domains are generalizations of Teichmüller spaces, and they admit some nice geometric and analytic properties (see [14][21]).”
• PROPERTIES OF SQUEEZING FUNCTIONS AND GLOBAL TRANSFORMATIONS OF BOUNDED DOMAINS (2013, methodology): “Consequently, by the work of Yeung in [25] and the results in §3, we have”