标题： 关于等周不等式的某些类似物 显示英文标题

标题： Some analogues of isoperimetric inequality

摘要： 离散等周不等式指出，在所有固定面积的 n 边形中，正 n 边形具有最小的周长。 我们证明了双曲几何中关于圆内接和切触多边形的离散等周不等式（涉及外接圆半径或内切圆半径）的类比，同时考虑单个多边形和多个多边形的情况。 此外，我们针对双曲几何中某些面积或周长受限的多个多边形，建立了两种等周不等式的版本。 显示英文摘要

摘要： The discrete isoperimetric inequality states that among all n -gons with a fixed area, the regular n -gon has the least perimeter. We prove analogues of the discrete isoperimetric inequality (involving circumradius or inradius) for cyclic and tangential polygons in hyperbolic geometry, considering both single and multiple polygons. Furthermore, we establish two versions of the isoperimetric inequality for multiple polygons in hyperbolic geometry with some restriction on their area or perimeter.