Compact embedded hypersurfaces with constant higher order anisotropic mean curvatures
| dc.creator | He, Yijun | |
| dc.creator | Li, Haizhong | |
| dc.creator | Ma, Hui | |
| dc.creator | Ge, Jianquan | |
| dc.date | 2007-12-05 | |
| dc.date | 2007-12-19 | |
| dc.date.accessioned | 2026-07-07T08:50:00Z | |
| dc.date.available | 2026-07-07T08:50:00Z | |
| dc.description | Given a positive function $F$ on $S^n$ which satisfies a convexity condition, for $1\leq r\leq n$, we define the $r$-th anisotropic mean curvature function $H^F_r$ for hypersurfaces in $\mathbb{R}^{n+1}$ which is a generalization of the usual $r$-th mean curvature function. We prove that a compact embedded hypersurface without boundary in $\R^{n+1}$ with $H^F_r={constant}$ is the Wulff shape, up to translations and homotheties. In case $r=1$, our result is the anisotropic version of Alexandrov Theorem, which gives an affirmative answer to an open problem of F. Morgan. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/0712.0694 | |
| dc.identifier | http://arxiv.org/abs/0712.0694 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144472 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C40 (Primary); 53A10, 52A20 (Secondary) | |
| dc.title | Compact embedded hypersurfaces with constant higher order anisotropic mean curvatures | |
| dc.type | text |