On Gromov's dihedral extremality and rigidity conjectures
Differential Geometry
2023-03-09 v6 K-Theory and Homology
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.
Cite
@article{arxiv.2112.01510,
title = {On Gromov's dihedral extremality and rigidity conjectures},
author = {Jinmin Wang and Zhizhang Xie and Guoliang Yu},
journal= {arXiv preprint arXiv:2112.01510},
year = {2023}
}
Comments
116 pages. Details for the index theorem of manifolds with polyhedral boundary have been provided