What question did this study set out to answer?

To explore uniform entropy bounds in Ricci shrinkers and extend non-collapsing results to smooth metric measure spaces.

February 8, 2026

Non-collapsing of Ricci shrinkers with bounded curvature

Key Points

To explore uniform entropy bounds in Ricci shrinkers and extend non-collapsing results to smooth metric measure spaces.
Establishes a uniform entropy bound for simply connected Ricci shrinkers.
Analyzes the effects of a finite second homotopy group in this context.
Extends results to a wider class of metric measure spaces under Bakry–Émery conditions.
Demonstrates the presence of a uniform entropy bound in Ricci shrinkers with bounded curvature.
Findings suggest the broader applicability of non-collapsing results to more general spaces.

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–Émery conditions.

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Cite This Study

Dong et al. (Thu,) studied this question.

synapsesocial.com/papers/6987eb5df6bacdd2fe8fc944 https://doi.org/https://doi.org/10.1007/s00208-026-03339-2

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