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Gromov’s dihedral rigidity conjecture and index theory on manifolds with corners

By Jinming Wang

In this talk, I will explain the key ideas of our recent work on positive solutions to Gromov's dihedral extremality and rigidity conjectures. One of the main ingredients is a new index theory on manifolds with corners (more generally, manifolds with polytope singularities), which is of independent interest on its own. Our approach is based on the analysis of differential operators arising from conical metrics. The comparison of dihedral angles enters into the study of these differential operators in an essential way. This is based on my joint works with Zhizhang Xie and Guoliang Yu.

Information about the video

  • Date of recording 01/04/2022
  • Date of publication 07/04/2022
  • Institution IHES
  • Language English
  • Audience Researchers
  • Format MP4

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