Isoperimetric inequalities in convex cylinders and cylindrically bounded convex bodies
Isoperimetric inequalities in convex cylinders and cylindrically bounded convex bodies
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凸圆柱和圆柱有界凸体的等周不等式
DOI：
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发表时间：
2014
期刊：
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通讯作者：
Efstratios Vernadakis
中科院分区：
文献类型：
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作者：
M. Ritoré;Efstratios Vernadakis
本文考虑凸柱K的等周轮廓 imes {mathbb {R}}^q$$K×Rq，其中$$K$$K是一个$$m维凸体，以及柱上有界凸集，即在$${mathbb {R}}^{n+1}$$Rn+1的某个超平面上具有相对紧的正交投影的凸集，渐近于形式为$$K的右凸柱 乘以{mathbb {R}}$$K×R，其中$$K子集{mathbb {R}}^n$$K <$Rn。结果有关的等周轮廓，存在的等周区域，等周区域的几何描述的小和大的体积。
In this paper we consider the isoperimetric profile of convex cylinders $$K imes {mathbb {R}}^q$$K×Rq, where $$K$$K is an $$m$$m-dimensional convex body, and of cylindrically bounded convex sets, i.e, those with a relatively compact orthogonal projection over some hyperplane of $${mathbb {R}}^{n+1}$$Rn+1, asymptotic to a right convex cylinder of the form $$K imes {mathbb {R}}$$K×R, with $$Ksubset {mathbb {R}}^n$$K⊂Rn. Results concerning the concavity of the isoperimetric profile, existence of isoperimetric regions, and geometric descriptions of isoperimetric regions for small and large volumes are obtained.