Year: 2026
Type: preprint
Abstract: For $n\ge2$, we prove a quantitative centre-rigidity estimate for bounded sets of finite Riemannian perimeter that are stationary and volume-constrained stable for normalized Riemannian perimeter with prescribed curvature $h_j$. Under confinement to a fixed compact set and cutoffs of vanishing full surface Dirichlet energy on the smooth regular boundary, the squared $L^2$ norms of the horizontal centre derivative, angle defect and weighted shape defect are bounded by $C(\varepsilon_j^2+\|h_j-2n\|_{C^2})|Ω_j|$ when the parenthesized quantity is sufficiently small. The excess of normalized Riemannian perimeter over horizontal perimeter satisfies the same bound.
Source: arXiv (Cornell University)
Authors: Chen, Wei-Chun, Kao, Wei-Ting, Lien, Chun-Kai
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220716359