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Workshop

Lipschitz rigidity for scalar curvature

  • Simone Cecchini
G3 10 (Lecture hall)

Abstract

I will discuss the following scalar curvature rigidity result for the round sphere in the low regularity setting. Let M be a closed smooth connected spin manifold of dimension n, and let g be a Riemannian metric on M of Sobolev regularity W1,p, for p>n, whose distributional scalar curvature in the sense of Lee-LeFloch is bounded below by n(n−1). Let f:(M,g)→Sn be a Lipschitz continuous map, that is area-nonincreasing almost everywhere and has non-zero degree. Then f is a metric isometry. In this talk, I will focus on the odd-dimensional case, using the analysis of Lipschitz Dirac operators on manifolds with conical singularities.

This is based on joint work with Bernhard Hanke, Thomas Schick, and Lukas Schoenlinner

Antje Vandenberg

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Alexandra Linde

Augsburg University Contact via Mail

Christian Bär

Potsdam University

Bernhard Hanke

Augsburg University

Anna Wienhard

Max Planck Institute for Mathematics in the Sciences

Burkhard Wilking

University of Münster