Asymptotic behavior of complete conformal metric near singular boundary
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916780847398912 |
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| author | Shen, Weiming Wang, Yue |
| author_facet | Shen, Weiming Wang, Yue |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04591 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic behavior of complete conformal metric near singular boundary Shen, Weiming Wang, Yue Analysis of PDEs Differential Geometry 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. |
| title | Asymptotic behavior of complete conformal metric near singular boundary |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2506.04591 |