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Extremality for the Vafa-Witten bound on the sphere

Marc Herzlich
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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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Marc Herzlich. 2004-11-29. Extremality for the Vafa-Witten bound on the sphere. https://arxiv.org/abs/math/0407530

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