Asymptotic behavior of complete conformal metric near singular boundary
Analysis of PDEs
2025-06-06 v1 Differential Geometry
Abstract
The boundary behavior of the singular Yamabe problem has been extensively studied near sufficiently smooth boundaries, while less is known about the asymptotic behavior of solutions near singular boundaries. In this paper, we study the asymptotic behaviors of solutions to the singular Yamabe problem with negative constant scalar curvature near singular boundaries and derive the optimal estimates for the background metric which is not necessarily conformally flat. In particular, we prove that the solutions are well approximated by the solutions in tangent cones at singular points on the boundaries.
Keywords
Cite
@article{arxiv.2506.04591,
title = {Asymptotic behavior of complete conformal metric near singular boundary},
author = {Weiming Shen and Yue Wang},
journal= {arXiv preprint arXiv:2506.04591},
year = {2025}
}
Comments
Published in Advances in Mathematics 458 (2024), Paper No. 109977, 34 pp