Hypersurfaces with constant anisotropic mean curvature in Riemannian manifolds
JHS de Lira, M Melo - Calculus of Variations and Partial Differential …, 2014 - Springer
JHS de Lira, M Melo
Calculus of Variations and Partial Differential Equations, 2014•SpringerWe 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.
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.
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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