Stein neighborhoods of graphs of holomorphic mappings

TL;DR

This paper establishes sufficient conditions under which the graphs of holomorphic mappings on compact sets in complex manifolds possess Stein neighborhoods, extending properties known for holomorphic functions in complex Euclidean spaces.

Contribution

It introduces new criteria ensuring the existence of Stein neighborhoods for graphs of holomorphic mappings in complex manifolds, generalizing classical results.

Findings

Graphs of holomorphic mappings have Stein neighborhoods under specified conditions.

Mappings exhibit properties similar to holomorphic functions on compact sets in ^n.

Provides a framework for understanding complex structures in manifold settings.

Abstract

In this paper we provide sufficient conditions for the graphs of holomorphic mappings on compact sets in complex manifolds to have Stein neighborhoods. We show that under these conditions the mappings have properties analogous to properties of holomorphic functions on compact sets in $\mathbb C^n$.