This note reveals a diffeomorphism criterion using Ricci flow, indicating improvements for manifolds with curvature concentration.
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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Huang et al. (2025) studied this question.
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