On Gromov's dihedral extremality and rigidity conjectures

Abstract

In this paper, we develop a new index theory for manifolds with polyhedral boundary. As an application, we prove Gromov's dihedral extremality conjecture regarding comparisons of scalar curvatures, mean curvatures and dihedral angles between two compact manifolds with polyhedral boundary in all dimensions. We also prove Gromov's dihedral rigidity conjecture for a class of positively curved manifolds with polyhedral boundary in all dimensions.

arXiv comment116 pages. Details for the index theorem of manifolds with polyhedral boundary have been provided

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