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

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.