Work

Visibility domains relative to the Kobayashi distance in complex manifolds

Year: 2025

Type: article

Abstract: In this paper, we extend the notion of visibility relative to the Kobayashi distance to domains in arbitrary complex manifolds. Visibility here refers to a property resembling visibility in the sense of Eberlein–O’Neill for Riemannian manifolds. Since it is difficult, in general, to determine whether domains are Cauchy-complete with respect to the Kobayashi distance, we do not assume so here. We provide many sufficient conditions for visibility. We establish a Wolff–Denjoy-type theorem in a very general setting as an application. We also explore some connections between visibility and Gromov hyperbolicity for Kobyashi hyperbolic domains in the above setting.

Source: Transactions of the American Mathematical Society

DOI: 10.1090/tran/9566

Author: Rumpa Masanta

Institution: Indian Institute of Science Bangalore

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Department of Science and Technology, Ministry of Science and Technology, India

Awards: G1488853880, G4733471938