Gap theorems for K\"ahler-Ricci solitons

TL;DR

This paper establishes that compact gradient shrinking K"ahler-Ricci solitons with excessively large Ricci curvature must be K"ahler-Einstein, providing a curvature gap criterion.

Contribution

It proves a new gap theorem linking Ricci curvature bounds to the K"ahler-Einstein condition in K"ahler-Ricci solitons.

Findings

Large Ricci curvature implies the soliton is K"ahler-Einstein.

Provides curvature bounds for compact K"ahler-Ricci solitons.

Advances understanding of curvature constraints in geometric analysis.

Abstract

In this paper, we prove that a gradient shrinking compact K\"ahler-Ricci soliton cannot have too large Ricci curvature unless it is K\"ahler-Einstein.