English

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

R2 v1 2026-07-22T20:14:44.348Z