关于立方体截面的体积

IF 0.9 3区数学 Q2 MATHEMATICS

Analysis and Geometry in Metric Spaces Pub Date : 2020-04-06 DOI:10.1515/agms-2020-0103

G. Ivanov, Igor Tsiutsiurupa

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引用次数: 10

摘要

摘要研究了n维立方体[−1,1]n的最大体积k维截面的性质。我们得到了k维子空间是这些截面的局部体积最大化的一阶必要条件，并以几何形式给出了这个条件。我们估计一个向量在一个k维子空间上的投影的长度，这个k维子空间使交点的体积最大化。我们找到了立方体平面截面体积的最优上界[−1,1]n, n≥2。

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On the Volume of Sections of the Cube

Abstract We study the properties of the maximal volume k-dimensional sections of the n-dimensional cube [−1, 1]n. We obtain a first order necessary condition for a k-dimensional subspace to be a local maximizer of the volume of such sections, which we formulate in a geometric way. We estimate the length of the projection of a vector of the standard basis of ℝn onto a k-dimensional subspace that maximizes the volume of the intersection. We find the optimal upper bound on the volume of a planar section of the cube [−1, 1]n, n ≥ 2.

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来源期刊

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.