PreprintarXiv licencearXiv
Scalar curvature rigidity of small spherical caps with arbitrary fill-ins
Abstract
We prove an analogue of Min-Oo's conjecture for sufficiently small spherical caps in the unit round sphere. For every dimension n≥3, there exists r*(n)>0 such that the following holds for every round cap of radius 0<r≤ r*(n): any smooth compact connected oriented Riemannian fill-in with the same intrinsic boundary metric and with scalar curvature and outward boundary mean curvature at least those of the cap is isometric to the cap.
Related
- Sharp local scalar-curvature rigidity of spherical caps
- Rigidity of Constant-Scalar-Curvature Ricci Shrinkers with Totally Geodesic Focal Set
- Scalar curvature bounds and rigidity of Ricci shrinkers
- Rigidity and weak notions of spectral scalar curvature
- Complete Self-Shrinkers in Arbitrary Codimension with Positive Constant Scalar Curvature and S≤ 1
BibTeX
@misc{zhang2026scalar,
title = {{Scalar curvature rigidity of small spherical caps with arbitrary fill-ins}},
author = {Yiyue Zhang and Bowen Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18413},
eprint = {2610.18413},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18413},
}
RIS
TY - UNPB
TI - Scalar curvature rigidity of small spherical caps with arbitrary fill-ins
AU - Yiyue Zhang
AU - Bowen Zhao
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18413
UR - https://arxiv.org/abs/2610.18413
AB - We prove an analogue of Min-Oo's conjecture for sufficiently small spherical caps in the unit round sphere. For every dimension n≥3, there exists r_*(n)>0 such that the following holds for every round cap of radius 0<r≤ r_*(n): any smooth compact connected oriented Riemannian fill-in with the same intrinsic boundary metric and with scalar curvature and outward boundary mean curvature at least those of the cap is isometric to the cap.
ER -