PreprintarXiv licencearXiv
Rigidity and weak notions of spectral scalar curvature
Abstract
We give a weak formulation of spectral scalar curvature bounded from below via establishing a dihedral rigidity result. Given some special convex polyhedron, if another metric are of non-negative spectral scalar curvature in the interior, with weighted mean-convex faces, and with its dihedral angles less than or equal to their flat polyhedral model everywhere along the edges, then the metric must be flat. This is motivated by Gromov's definition of a weak notion of non-negative scalar curvature.
Related
- Rigidity of Constant-Scalar-Curvature Ricci Shrinkers with Totally Geodesic Focal Set
- Scalar curvature bounds and rigidity of Ricci shrinkers
- Scalar curvature rigidity of small spherical caps with arbitrary fill-ins
- Rigidity of nonsteady gradient Kähler-Ricci solitons with constant scalar curvature
- Integral of Scalar Curvature: Sharp Asymptotic Bounds and Rigidity
BibTeX
@misc{chai2026rigidity,
title = {{Rigidity and weak notions of spectral scalar curvature}},
author = {Xiaoxiang Chai},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21721},
eprint = {2609.21721},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21721},
}
RIS
TY - UNPB
TI - Rigidity and weak notions of spectral scalar curvature
AU - Xiaoxiang Chai
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21721
UR - https://arxiv.org/abs/2609.21721
AB - We give a weak formulation of spectral scalar curvature bounded from below via establishing a dihedral rigidity result. Given some special convex polyhedron, if another metric are of non-negative spectral scalar curvature in the interior, with weighted mean-convex faces, and with its dihedral angles less than or equal to their flat polyhedral model everywhere along the edges, then the metric must be flat. This is motivated by Gromov's definition of a weak notion of non-negative scalar curvature.
ER -