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Localization of the Kobayashi metric and applications (2004.07421v1)
Published 16 Apr 2020 in math.CV
Abstract: In this paper we introduce a new class of domains -- log-type convex domains, which have no boundary regularity assumptions. Then we will localize the Kobayashi metric in log-type convex subdomains. As an application, we prove a local version of continuous extension of rough isometric maps between two bounded domains with log-type convex Dini-smooth boundary points. Moreover we prove that the Teichm\"uller space $\mathcal T_{g,n}$ is not biholomorphic to any bounded pseudoconvex domain in $\mathbb C{3g-3+n}$ which is locally log-type convex near some boundary point.