Conformal Scalar-Flat Metrics with Prescribed Boundary Mean Curvature
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916041711419392 |
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| author | Shen, Jiashu Sheng, Hongyi |
| author_facet | Shen, Jiashu Sheng, Hongyi |
| contents | Let $(M, g)$ be a compact Riemannian manifold with boundary $\partial M$. Given a function $f$ on $\partial M$, we consider the problem of finding a conformal metric of $g$ with zero scalar curvature in $M$ and prescribed mean curvature $f$ on $\partial M$. Through the construction of local test functions, we resolve most of the remaining open cases from Escobar's work and establish new solvability conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_06302 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conformal Scalar-Flat Metrics with Prescribed Boundary Mean Curvature Shen, Jiashu Sheng, Hongyi Differential Geometry Let $(M, g)$ be a compact Riemannian manifold with boundary $\partial M$. Given a function $f$ on $\partial M$, we consider the problem of finding a conformal metric of $g$ with zero scalar curvature in $M$ and prescribed mean curvature $f$ on $\partial M$. Through the construction of local test functions, we resolve most of the remaining open cases from Escobar's work and establish new solvability conditions. |
| title | Conformal Scalar-Flat Metrics with Prescribed Boundary Mean Curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2410.06302 |