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arXiv · 2404.17533

Rigidity of spin fill-ins with non-negative scalar curvature

Simone Cecchini·Sven Hirsch·Rudolf Zeidler
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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.

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Simone Cecchini, Sven Hirsch, Rudolf Zeidler. 2024-04-26. Rigidity of spin fill-ins with non-negative scalar curvature. https://arxiv.org/abs/2404.17533

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