Stability of hypersurfaces with constant $r$-th anisotropic mean curvature
| dc.creator | He, Yijun | |
| dc.creator | Li, Haizhong | |
| dc.date | 2008-01-23 | |
| dc.date.accessioned | 2026-07-07T08:56:04Z | |
| dc.date.available | 2026-07-07T08:56:04Z | |
| dc.description | Given a positive function $F$ on $S^n$ which satisfies a convexity condition, 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. Let $X:M\to \mathbb{R}^{n+1}$ be an $n$-dimensional closed hypersurface with $H^F_{r+1}=$constant, for some $r$ with $0\leq r\leq n-1$, which is a critical point for a variational problem. We show that $X(M)$ is stable if and only if $X(M)$ is the Wulff shape. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/0801.3561 | |
| dc.identifier | http://arxiv.org/abs/0801.3561 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146480 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C42, 53A10 (Primary); 49Q10 (Secondary) | |
| dc.title | Stability of hypersurfaces with constant $r$-th anisotropic mean curvature | |
| dc.type | text |