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Extremality for the Vafa–Witten bound on the sphere

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Abstract.

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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Authors and Affiliations

  1. Institut de Mathématiques et Modélisation de Montpellier, UMR 5149 du CNRS, Université Montpellier II, Montpellier Cedex 05, France

    M. Herzlich

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  1. M. Herzlich
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Correspondence to M. Herzlich.

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Received: July 2004 Revision: October 2004 Accepted: November 2004

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Herzlich, M. Extremality for the Vafa–Witten bound on the sphere. GAFA, Geom. funct. anal. 15, 1153–1161 (2005). https://doi.org/10.1007/s00039-005-0536-5

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  • DOI: https://doi.org/10.1007/s00039-005-0536-5

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