Visibility domains relative to the Kobayashi distance in complex manifolds

Rumpa Masanta

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arXiv · 2406.09376

Visibility domains relative to the Kobayashi distance in complex manifolds

Rumpa Masanta

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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 Kobayashi hyperbolic domains in the above setting.

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Rumpa Masanta. 2024-06-13. Visibility domains relative to the Kobayashi distance in complex manifolds. https://arxiv.org/abs/2406.09376

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