کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4605940 1337671 2014 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Constant mean curvature polytopes and hypersurfaces via projections
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Constant mean curvature polytopes and hypersurfaces via projections
چکیده انگلیسی

Given a regular polytope in Euclidean space and an orthogonal projection to the complex plane, the function which assigns to each vertex its projected value satisfies a quadratic difference equation. The form of the equation is the same, whatever the polytope, except for a real parameter ρ which varies from polytope to polytope. It is independent of the projection used and the size of the polytope. When we consider an orthogonal projection of a smooth hypersurface in Euclidean space, remarkably we find the same phenomena, namely that a smooth version of the equation is satisfied independently of the projection, where the parameter ρ depends only on the mean curvature. We therefore make an unconventional definition of a constant mean-curvature polytope as one which satisfies this same equation with ρ constant, independently of the orthogonal projection. We discuss some examples of constant mean curvature polytopes.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Differential Geometry and its Applications - Volume 33, Supplement, March 2014, Pages 199–212
نویسندگان
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