References & Citations
Mathematics > Differential Geometry
Title: Rigidity of spin fill-ins with non-negative scalar curvature
(Submitted on 26 Apr 2024 (v1), last revised 14 May 2024 (this version, v2))
Abstract: We establish new mean curvature rigidity theorems of 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.
Submission history
From: Rudolf Zeidler [view email][v1] Fri, 26 Apr 2024 16:57:52 GMT (46kb,D)
[v2] Tue, 14 May 2024 13:51:44 GMT (36kb,D)
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