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October 3, 2025Open Access

A note on a diffeomorphism criterion via long-time Ricci flow

Key Points

Establishing a diffeomorphism criterion via Ricci flow yields improved conditions for certain manifolds.
The study confirms improvements in dimensions, particularly dimension 4, for manifolds with small curvature concentration.
Applications extend previous work, linking curvature conditions to diffeomorphic properties of manifolds.
This approach enhances understanding of geometric flows, specifically Ricci flow, in the context of manifolds.

Abstract

In this note, we give a diffeomorphism (to Rⁿ) criterion via long-time Ricci flow and show some applications. In particular, we provide an affirmative answer that the conclusion in Manifolds with small curvature concentration, Ann. PDE, 2024 by Chan, Lee and the first named author and Removing scalar curvature assumption for Ricci flow smoothing, Bull. Lond. Math. Soc. , 2025 by A. Martens about manifolds with small curvature concentration can be improved to diffeomorphism in dimension 4.

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Authors

Shaochuang Huang

Sun Yat-sen University

Zhengqiang Peng

Chinese Academy of Tropical Agricultural Sciences

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A note on a diffeomorphism criterion via long-time Ricci flow

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