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Estimates for stable hypersurfaces of prescribed F-mean curvature

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Abstract

We consider immersed hypersurfaces :M n→ℝn +1 with prescribed anisotropic mean curvature . Such hypersurfaces can be characterized as critical points of parametric functionals of the type with an elliptic Lagrangian F depending on normal directions and a smooth vectorfield Q satisfying . We establish curvature estimates for stable hypersurfaces of dimension n≤5, provided F is C 3-close to the area integrand.

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  1. Centro di Ricerca, Mathematica Ennio De Giorgi, Scuola Normale Superiore di Pisa, 56100, Pisa, Italy

    Sven Winklmann

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  1. Sven Winklmann
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Winklmann, S. Estimates for stable hypersurfaces of prescribed F-mean curvature. manuscripta math. 118, 485–499 (2005). https://doi.org/10.1007/s00229-005-0600-3

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  • DOI: https://doi.org/10.1007/s00229-005-0600-3

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