Quantitative Stability for Minimizing Yamabe Metrics with minimal boundary
Differential Geometry
2026-05-27 v2
Abstract
In this paper, we investigate the stability of minimizing Yamabe metrics on compact manifolds with boundary, in the sense introduced by Escobar. We show that if a function nearly minimizes the Yamabe energy, then the associated conformal metric is quantitatively close to a minimizing Yamabe metric within its conformal class. Moreover, this closeness is controlled by an appropriate power of the Yamabe energy deficit.
Keywords
Cite
@article{arxiv.2605.17191,
title = {Quantitative Stability for Minimizing Yamabe Metrics with minimal boundary},
author = {Runze Lin and Bao Yu},
journal= {arXiv preprint arXiv:2605.17191},
year = {2026}
}
Comments
We add the remark 1.4 about an example with super quadratic growth