非欧几里得多边形的等周不等式

arXiv - MATH - Metric Geometry Pub Date : 2024-09-10 DOI:arxiv-2409.06529

Basudeb Datta, Subhojoy Gupta

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引用次数: 0

摘要

欧几里得几何中的一个经典事实是，在周长和边数相同的多边形中，正多边形的面积最大。在本论文中，我们提出了双曲几何和球面几何中多边形面积不等式的完整证明。

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Isoperimetric inequality for non-Euclidean polygons

It is a classical fact in Euclidean geometry that the regular polygon maximizes area amongst polygons of the same perimeter and number of sides, and the analogue of this in non-Euclidean geometries has long been a folklore result. In this note, we present a complete proof of this polygonal isoperimetric inequality in hyperbolic and spherical geometries.

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arXiv - MATH - Metric Geometry

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