Approximation of smooth convex bodies by circumscribed polytopes with respect to the surface area
Approximation of smooth convex bodies by circumscribed polytopes with respect to the surface area
复制标题
光滑凸体的外接多面体关于表面积的近似
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
B. Csikós
中科院分区：
文献类型：
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作者：
K. Böröczky;B. Csikós
设K是欧氏d-空间中具有C2边界的凸体。在L.Fejes Tóth，R.Vitale，R.Schneider，P.M.Gruber，S.Glasauer和M.Ludwig的工作之后，如果K的最佳逼近是关于体积或平均宽度的，则K的最佳逼近是很好地理解的。本文考虑具有最小表面积的n个面片的外接多面体P(N)，给出了表面积与K的表面积之差以n表示的渐近公式。
Let K be a convex body with C2 boundary in the Euclidean d-space. Following the work of L. Fejes Tóth, R. Vitale, R. Schneider, P.M. Gruber, S. Glasauer and M. Ludwig, best approximation of K by polytopes of restricted number of vertices or facets is well-understood if the approximation is with respect to the volume or the mean width. In this paper we consider the circumscribed polytope P(n) of n facets with minimal surface area, and present an asymptotic formula in terms of n for the difference of surface areas of P(n) and K.