Non-collapsing of Ricci shrinkers with bounded curvature

TL;DR

This paper proves a uniform entropy bound for certain Ricci shrinkers with bounded curvature and extends non-collapsing results to a wider class of smooth metric measure spaces under Bakry-Emery conditions.

Contribution

It introduces a uniform entropy bound for Ricci shrinkers with finite second homotopy group and extends non-collapsing results to broader metric measure spaces.

Findings

Established a uniform entropy bound for Ricci shrinkers.

Extended non-collapsing results to Bakry-Emery spaces.

Applicable to Ricci shrinkers with bounded curvature and specific topological conditions.

Abstract

We establish a uniform entropy bound for simply connected Ricci shrinkers with a finite second homotopy group and a uniform curvature bound. Additionally, we extend the non-collapsing result to a broader class of smooth metric measure spaces satisfying Bakry-\'Emery conditions.