不连通区域的等周不等式
Isoperimetric Inequality for Disconnected Regions
AI总结：
本文将欧氏、球面和双曲几何中适用于单$n$边形的离散等周不等式推广到不连通区域，给出了面积累加的多个$n$边形满足该不等式的充要条件。
摘要：
欧氏几何中的离散等周不等式指出，在所有周长固定为$p$的$n$边形中，面积最大的是正$n$边形。该结论在球面几何和双曲几何中同样成立。本文将离散等周不等式推广到不连通区域的情形，即允许面积被拆分到多个区域中。我们给出了该结果在欧氏、球面和双曲几何中对面积累加的多个$n$边形成立的充要条件。
英文摘要：
The discrete isoperimetric inequality in Euclidean geometry states that among all $n$-gons having a fixed perimeter $p$, the one with the largest area is the regular $n$-gon. The statement is true in spherical geometry and hyperbolic geometry as well. In this paper, we generalize the discrete isoperimetric inequality to disconnected regions, i.e. we allow the area to be split between regions. We give necessary and sufficient conditions for the result (in Euclidean, spherical and hyperbolic geometry) to hold for multiple $n$-gons whose areas add up.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
