Geometry of domains with the uniform squeezing property

Details Geometry of domains with the uniform squeezing property Geometry of domains with the uniform squeezing property

2009-06-25

arxiv.org/abs/0906.4647v1

Advances in Mathematics 221(2009) 547-569

Mathematics

Complex Variables

Scientific paper

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, Kaehler-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.

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