Scalar curvature rigidity of the four-dimensional sphere
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.
Authors
- Bo Zhu (ORCID: https://orcid.org/0000-0001-8908-5327)
- S. Cecchini (ORCID: https://orcid.org/0000-0002-9757-3141)
- Zhizhang Xie
- Jinmin Wang
Institutions
- Institute of Physics (CN)
- Texas A&M University (US)
- Tsinghua University (CN)
Publication Details
- Journal
- Mathematische Annalen
- Published
- 2026-02-18
- DOI
- https://doi.org/10.1007/s00208-026-03385-w
- Primary Topic
- Geometric Analysis and Curvature Flows
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- National Natural Science Foundation of China