Kobayashi complete domains in complex manifolds

TL;DR

This paper establishes new sufficient conditions for the Cauchy-completeness of Kobayashi hyperbolic domains within complex manifolds, extending previous results to broader classes of manifolds.

Contribution

It provides generalized sufficient conditions for Kobayashi completeness, extending Gaussier's results to more general complex manifold settings.

Findings

Sufficient conditions for completeness of relatively compact domains

Extension of Gaussier's results to broader manifold classes

General framework applicable to various complex manifolds

Abstract

In this paper, we give sufficient conditions for Cauchy-completeness of Kobayashi hyperbolic domains in complex manifolds. The first result gives a sufficient condition for completeness for relatively compact domains in several large classes of manifolds. This follows from our second result, which may be of independent interest, in a much more general setting. This extends a result of Gaussier to the setting of manifolds.