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On Gromov’s rigidity theorem for polytopes with acute angles

By Yipeng Wang

In his Four Lectures, Gromov formulated a conjecture regarding the scalar curvature extremality property of convex polytopes. Recently, assuming the matching angle hypothesis, S. Brendle provided a proof using Dirac operator techniques along with a smoothing construction. Additionally, Gromov outlined a proof of this conjecture, specifically addressing cases with acute dihedral angles. In this presentation, I will provide a brief summary of recent developments in the dihedral rigidity problem. I will also discuss joint work with S. Brendle, where we introduce an alternative smoothing construction for Gromov's argument. Our proof of the rigidity statement relies on a deep estimate due to Fefferman and Phong.

Information about the video

  • Date of recording 18/10/2023
  • Date of publication 14/11/2023
  • Institution IHES
  • Language English
  • Audience Researchers
  • Format MP4


S. Brendle, Y. Wang. On Gromov's rigidity theorem for polytopes with acute angles. arXiv:2308.08000

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