包含在圆盘中的凸多边形幂矩的极值问题

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2021-10-01 DOI:10.1515/advgeom-2021-0021

I. Herburt, S. Sakata

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引用次数: 0

摘要

摘要本文研究了圆盘上凸多边形幂矩的极值问题。我们的结果是一个经典定理的推广:在给定圆盘中包含的所有凸n-gon中，在圆内的正则n-gon(直到旋转)唯一地最大化了泛函面积。它还意味着，在给定圆盘中包含的所有凸n-gon中，在这些内部包含中心，在圆内的规则n-gon(直到旋转)唯一地最大化通过圆盘中心的弦长度的平均值。

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An extremum problem for the power moment of a convex polygon contained in a disc

Abstract In this paper, we investigate an extremum problem for the power moment of a convex polygon contained in a disc. Our result is a generalization of a classical theorem: among all convex n-gons contained in a given disc, the regular n-gon inscribed in the circle (up to rotation) uniquely maximizes the area functional. It also implies that, among all convex n-gons contained in a given disc and containing the center in those interiors, the regular n-gon inscribed in the circle (up to rotation) uniquely maximizes the mean of the length of the chords passing through the center of the disc.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.