Stability of hypersurfaces with constant (r+1)-th anisotropic mean curvature
Yijun He and Haizhong Li
Source: Illinois J. Math. Volume 52, Number 4 (2008), 1301-1314.
Abstract
Given a positive function F on Sn which satisfies a convexity condition, we define the r-th anisotropic mean curvature function HrF for hypersurfaces in ℝn+1 which is a generalization of the usual r-th mean curvature function. Let X : M→ℝn+1 be an n-dimensional closed hypersurface with Hr+1F=constant, for some r with 0≤r≤n−1, which is a critical point for a variational problem. We show that X(M) is stable if and only if X(M) is the Wulff shape.
Primary Subjects: 53C42, 53A10, 49Q10
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ijm/1258554364
Zentralblatt MATH identifier:
05660660
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