Hypersurfaces with constant anisotropic mean curvature in Riemannian manifolds |
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Authors: | Jorge H. S. de Lira Marcelo Melo |
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Affiliation: | 1. Department of Mathematics, Federal University of Ceará, Campus do Pici, Ceará, Fortaleza, 60455-900, Brasil
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Abstract: | We formulate a variational notion of anisotropic mean curvature for immersed hypersurfaces of arbitrary Riemannian manifolds. Hypersurfaces with constant anisotropic mean curvature are characterized as critical points of an elliptic parametric functional subject to a volume constraint. We provide examples of such hypersurfaces in the case of rotationally invariant functionals defined in product spaces. These examples include rotationally invariant hypersurfaces and graphs. |
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