# Complete open Kahler manifolds with nonnegative bisectional curvature and non-maximal volume growth

## TL;DR

This paper investigates conditions under which complete open Kähler manifolds with nonnegative bisectional curvature are Stein, focusing on volume growth restrictions to partially resolve an open problem.

## Contribution

It introduces a weaker volume growth condition that extends previous results, advancing understanding of the structure of such Kähler manifolds.

## Key findings

- Established partial criteria for Steinness under volume growth restrictions
- Improved previous observations on volume growth conditions
- Provided new insights into the geometry of nonnegative bisectional curvature manifolds

## Abstract

It is still an open problem that a complete open Kahler manifold with positive bisectional curvature is Stein. This paper partially resolve the problem by putting a restriction to volume growth condition. The partial solution here improves the observation in ([8], page 341). The improvement is based on assuming a weaker volume growth condition that is not sufficiently maximal.