Stability of Llarull's theorem in all dimensions
Abstract
Llarull's theorem characterizes the round sphere $S^n$ among all spin manifolds whose scalar curvature is bounded from below by $n(n1)$. In this paper we show that if the scalar curvature is bounded from below by $n(n1)\varepsilon$, the underlying manifold is $C^0$close to a finite number of spheres outside a small bad set. This completely solves Gromov's spherical stability problem.
 Publication:

arXiv eprints
 Pub Date:
 October 2023
 DOI:
 10.48550/arXiv.2310.14412
 arXiv:
 arXiv:2310.14412
 Bibcode:
 2023arXiv231014412H
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Analysis of PDEs;
 53C27;
 53C24