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