Work

Scalar curvature rigidity of the four-dimensional sphere

Year: 2026

Type: article

Abstract: Let ( M , g ) be a four-dimensional closed connected oriented (possibly non-spin) Riemannian manifold whose scalar curvature is bounded below by 12. We prove that, if f is a smooth distance non-increasing map of non-zero degree from ( M , g ) to the unit four-sphere, then f is an isometry. This removes the spin condition in Llarull’s scalar curvature rigidity theorem for spheres in dimension four.

Source: Mathematische Annalen

DOI: 10.1007/s00208-026-03385-w

Authors: Simone Cecchini, Jinmin Wang, Zhizhang Xie, Bo Zhu

Institutions: Texas A&M University, Chinese Academy of Sciences, Tsinghua University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: National Science Foundation, National Natural Science Foundation of China