Caccioppoli's inequalities on constant mean curvature hypersurfaces in Riemannian manifolds

Autor:	Ilias, Said, Nelli, Barbara, Soret, Marc
Rok vydání:	2011
Předmět:	Mathematics - Differential Geometry 53A10 53C40 53C42 58E15
Druh dokumentu:	Working Paper
Popis:	This is a revised version (minor changes and a deeper insight in the positive curvature case). We prove some Caccioppoli's inequalities for the traceless part of the second fundamental form of a complete, noncompact, finite index, constant mean curvature hypersurface of a Riemannian manifold, satisfying some curvature conditions. This allows us to unify and clarify many results scattered in the literature and to obtain some new results. For example, we prove that there is no stable, complete, noncompact hypersurface in ${\mathbb R}^{n+1},$ $n\leq 5,$ with constant mean curvature $H\not=0,$ provided that, for suitable $p,$ the $L^p$-norm of the traceless part of second fundamental form satisfies some growth condition. Comment: 31 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1107.3653 Zobrazit plný text záznamu View this record from Arxiv