https://neckpinch.com/authors/zhizhang-xie/New arXiv papers by Zhizhang Xie, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2402.12633/arxiv:2402.12633Tue, 20 Feb 2024 00:00:00 GMTSimone Cecchini, Jinmin Wang, Zhizhang Xie, Bo Zhu — Let (M,g) be a closed connected oriented (possibly non-spin) smooth four-dimensional manifold with scalar curvature bounded below by n(n-1). In this paper, we prove that if f is a smooth map of non-zero degree from (M, g) to the unit four-sphere, then f is an isometry. Following ideas of Gromov, we use μ-bubbles and a version with coefficients of the rigidity of the three-sphere to rule out the case of strict inequality. Our proof of rigidity is based on the harmonic map heat flow coupled with the Ricci flow.Ricci flow4-manifoldsScalar curvatureStability & uniquenessHarmonic maps & DeTurck trick