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

Abstract : 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 Rn+1, n ≤ 5, with constant mean curvature H 6= 0, provided that, for suitable p, the Lp-norm of the traceless part of second fundamental form satisfies some growth condition.
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Article dans une revue
Ann. Global Anal. Geom., 2012, 42 (4), pp.443-471
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https://hal.archives-ouvertes.fr/hal-00849270
Contributeur : Marc Soret <>
Soumis le : mardi 30 juillet 2013 - 15:19:54
Dernière modification le : samedi 9 juin 2018 - 01:17:17

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  • HAL Id : hal-00849270, version 1

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Marc Soret, Said Ilias, Barbara Nelli, Marc Soret, Marc Soret. Caccioppoli's inequalities on constant mean curvature hypersurfaces in Riemannian manifolds. Ann. Global Anal. Geom., 2012, 42 (4), pp.443-471. 〈hal-00849270〉

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