Extremality for the Vafa–Witten bound on the sphere

We prove that the round metric on the sphere has the largest first eigenvalue of the Dirac operator among all metrics that are larger than it. As a corollary, this gives an alternative proof of an extremality result for scalar curvature due to M. Llarull.

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Bibliographic Details
Published in:Geometric and functional analysis 2005-12, Vol.15 (6), p.1153-1161
Main Author: Herzlich, M.
Format: Article
Language:English
Subjects:
Differential Geometry
Eigenvalues
Mathematics
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Description
Summary:We prove that the round metric on the sphere has the largest first eigenvalue of the Dirac operator among all metrics that are larger than it. As a corollary, this gives an alternative proof of an extremality result for scalar curvature due to M. Llarull.
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-005-0536-5