What question did this study set out to answer?

The aim is to establish a criterion for diffeomorphism using long-time Ricci flow.

March 12, 2026

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

Key Points

The aim is to establish a criterion for diffeomorphism using long-time Ricci flow.
Utilized long-time Ricci flow techniques to analyze manifold structures.
Examined curvature concentration properties in dimension 4.
Compared findings with previous works by Chan, Huang, Lee, and Martens.
Confirmed that the diffeomorphism conclusion about small curvature concentration is valid for dimension 4.
Provided improvements on previously established results in the referred literature.

Abstract

Abstract In this note, we give a diffeomorphism (to ) criterion via long‐time Ricci flow and show some applications. In particular, we provide an affirmative answer that the conclusion in Chan, Huang, and Lee Ann. PDE 10 (2024), no. 2, Paper No. 23, 31 and Martens Bull. London Math. Soc. 57 (2025), no. 7, 1968–1989 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

Zhuo Peng

Sun Yat-sen University

Journals

Bulletin of the London Mathematical Society

Actions

Institutions

Sun Yat-sen University

Shenzhen University

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Cite this study

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

synapsesocial.com/papers/69b2586696eeacc4fcec7fa5 — DOI: https://doi.org/10.1112/blms.70321

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Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

Local mollification of Riemannian metrics using Ricci flow, and Ricci limit spaces· 2021 · 30 citations
Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds· 1982 · 860 citations
Chern–Ricci flows on noncompact complex manifolds· 2020 · 19 citations
On the structure of spaces with Ricci curvature bounded below. I· 1997 · 921 citations
Three-manifolds with positive Ricci curvature· 1982 · 3,023 citations

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

Key Points

Abstract

Citation Network

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Discussion

Authors

Journals

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Institutions

References and Citations

Citation Network

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Discussion

Cite this study

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Also consider