Gromov's dihedral rigidity conjecture in dimension three
Differential Geometry
2026-06-29 v1 K-Theory and Homology
Abstract
In this article, we present a self-contained proof of Gromov's dihedral rigidity conjecture on scalar curvature in the three-dimensional case. The proof avoids many of the technical complications that arise in higher dimensions, while still illustrating the essential ideas of the general approach developed in arXiv:2112.01510 (version 6) and arXiv:2203.09511. It is significantly shorter than the proof of the general case and is intended to be more accessible.
Cite
@article{arxiv.2606.30130,
title = {Gromov's dihedral rigidity conjecture in dimension three},
author = {Jinmin Wang and Zhizhang Xie and Guoliang Yu},
journal= {arXiv preprint arXiv:2606.30130},
year = {2026}
}
Comments
74 pages, 15 figures. Comments are welcome