Solutions of the singular Yamabe problem near singular boundaries
Analysis of PDEs
2026-02-17 v2
Abstract
In this paper, we investigate the asymptotic behaviors of solutions to the singular Yamabe problem with negative constant scalar curvature near singular boundaries and derive optimal estimates, where the background metrics are not assumed to be conformally flat. Specifically, we demonstrate that for a wide class of Lipschitz domains with asymptotic conical structure, the local positive solutions are well approximated by the positive solutions in the tangent cones at singular boundary points. This extends the results of [10, 12, 26].
Cite
@article{arxiv.2512.23331,
title = {Solutions of the singular Yamabe problem near singular boundaries},
author = {Weiming Shen and Zhehui Wang and Jiongduo Xie},
journal= {arXiv preprint arXiv:2512.23331},
year = {2026}
}
Comments
This version includes improvements to Theorem 1.3 and Lemma 4.1, as well as corrections of some typos