Compact embedded hypersurfaces with constant higher order anisotropic mean curvatures
نویسندگان
چکیده
Given a positive function F on S which satisfies a convexity condition, for 1 ≤ r ≤ n, we define the r-th anisotropic mean curvature function H r for hypersurfaces in R which is a generalization of the usual r-th mean curvature function. We prove that a compact embedded hypersurface without boundary in R with H r = constant is the Wulff shape, up to translations and homotheties. In case r = 1, our result is the anisotropic version of Alexandrov Theorem, which gives an affirmative answer to an open problem of F. Morgan. 2000 Mathematics Subject Classification: Primary 53C40; Secondary 53A10, 52A20.
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تاریخ انتشار 2007