Stability of hypersurfaces with constant $(r+1)$-th anisotropic mean curvature

Stability of Hypersurfaces with Constant R-th Anisotropic Mean Curvature

Given a positive function F on S which satisfies a convexity condition, we define the r-th anisotropic mean curvature function H r for hypersurfaces in R n+1 which is a generalization of the usual r-th mean curvature function. Let X : M → R be an n-dimensional closed hypersurface with H r+1 =constant, for some r with 0 ≤ r ≤ n− 1, which is a critical point for a variational problem. We show tha...

STABILITY OF HYPERSURFACES WITH CONSTANT (r+ 1)-TH ANISOTROPIC MEAN CURVATURE

Given a positive function F on S which satisfies a convexity condition, we define the r-th anisotropic mean curvature function H r for hypersurfaces in R n+1 which is a generalization of the usual r-th mean curvature function. LetX : M → R n+1 be an n-dimensional closed hypersurface with H r+1 = constant, for some r with 0≤ r ≤ n− 1, which is a critical point for a variational problem. We show ...

Ja n 20 08 STABILITY OF HYPERSURFACES WITH CONSTANT R - TH ANISOTROPIC MEAN CURVATURE

Given a positive function F on S which satisfies a convexity condition, we define the r-th anisotropic mean curvature function H r for hypersurfaces in R n+1 which is a generalization of the usual r-th mean curvature function. Let X : M → R be an n-dimensional closed hypersurface with H r+1 =constant, for some r with 0 ≤ r ≤ n− 1, which is a critical point for a variational problem. We show tha...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

hypersurfaces with constant mean curvature in a lorentzian space form