Goldilocks domains, a weak notion of visibility, and applications

Bharali, Gautam and Zimmer, Andrew (2017) Goldilocks domains, a weak notion of visibility, and applications. In: ADVANCES IN MATHEMATICS, 310 . pp. 377-425.

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Abstract

In this paper we introduce a new class of domains in complex Euclidean space, called Goldilocks domains, and study their complex geometry. These domains are defined in terms of a lower bound on how fast the Kobayashi metric grows and an upper bound on how fast the Kobayashi distance grows as one approaches the boundary. Strongly pseudoconvex domains and weakly pseudoconvex domains of finite type always satisfy this Goldilocks condition, but we also present families of Goldilocks domains that have low boundary regularity or have boundary points of infinite type. We will show that the Kobayashi metric on these domains behaves, in some sense, like a negatively curved Riemannian metric. In particular, it satisfies a visibility condition in the sense of Eberlein and O'Neill. This behavior allows us to prove a variety of results concerning boundary extension of maps and to establish Wolff-Denjoy theorems for a wide collection of domains. (C) 2017 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Publication:	ADVANCES IN MATHEMATICS
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE, 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA
Additional Information:	Copy right for this article belongs to the ACADEMIC PRESS INC ELSEVIER SCIENCE, 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	20 May 2017 04:20
Last Modified:	20 May 2017 04:20
URI:	http://eprints.iisc.ac.in/id/eprint/56848

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