A Condition in Mean Curvature Prescriptions for Conformal Metrics on the Ball
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2013
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| _version_ | 1866912104889450496 |
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| author | Ortiz, Alvaro Garcia, Gonzalo |
| author_facet | Ortiz, Alvaro Garcia, Gonzalo |
| contents | This paper considers the prescribed zero scalar curvature and mean curvature problem on the n-dimensional Euclidean ball for $n \geq 3$. Given a rotationally symmetric function $H:\partial B^{n}\rightarrow R$, in this work, we will prove that if $H'(r)$ changes signs where $H>0$ and $H(r)$ also satisfies a flatness condition then there exists a metric $g$ conformal to the Euclidean metric, with zero scalar curvature in the ball and mean curvature $H$ on its boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1301_0945 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | A Condition in Mean Curvature Prescriptions for Conformal Metrics on the Ball Ortiz, Alvaro Garcia, Gonzalo Differential Geometry This paper considers the prescribed zero scalar curvature and mean curvature problem on the n-dimensional Euclidean ball for $n \geq 3$. Given a rotationally symmetric function $H:\partial B^{n}\rightarrow R$, in this work, we will prove that if $H'(r)$ changes signs where $H>0$ and $H(r)$ also satisfies a flatness condition then there exists a metric $g$ conformal to the Euclidean metric, with zero scalar curvature in the ball and mean curvature $H$ on its boundary. |
| title | A Condition in Mean Curvature Prescriptions for Conformal Metrics on the Ball |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/1301.0945 |