Rigidity of spin fill-ins with non-negative scalar curvature
Abstract
We establish new mean curvature rigidity theorems for spin fill-ins with non-negative scalar curvature using two different spinorial techniques. Our results address two questions by Miao and Gromov, respectively. The first technique is based on extending boundary spinors satisfying a generalized eigenvalue equation via the Fredholm alternative for an APS boundary value problem, while the second is a comparison result in the spirit of Llarull and Lott using index theory. We also show that the latter implies a new Witten-type integral inequality for the mass of an asymptotically Schwarzschild manifold, which holds even when the scalar curvature is not assumed to be non-negative.
Keywords
Cite
@article{arxiv.2404.17533,
title = {Rigidity of spin fill-ins with non-negative scalar curvature},
author = {Simone Cecchini and Sven Hirsch and Rudolf Zeidler},
journal= {arXiv preprint arXiv:2404.17533},
year = {2026}
}
Comments
24 pages; v2: additional result in section 3 and miscellaneous minor improvements; v3: miscellaneous improvements to the exposition