科研之友
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摘要
Given a positive function F on S(n) which satisfies a convexity condition, we define the rth anisotropic mean curvature function M(r) for hypersurfaces in R(n+1) which is a generalization of the usual rth mean curvature function. Let X: M --> R(n+1) be an n-dimensional closed hypersurface with M(r+1)/M(r) = constant, for some r with 1 <= r <= n - 1, which is a critical point for a variational problem. We show that X(M) is stable if an only if X(M) is the Wulff shape.
