This note demonstrates a diffeomorphism criterion in dimension 4, improving previous results on curvature concentration.
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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Huang et al. (2026) studied this question.
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