关于多边形等周不等式的稳定性
On the stability of the polygonal isoperimetric inequality
摘要：
我们得到了一般多边形的等周亏度的一个精确的下界，它的边长的方差，它的半径的方差，它的偏离凸。我们的技术涉及一个适当构造的紧凑的流形上的功能最小化问题，是基于循环矩阵的谱理论。
英文摘要：
We obtain a sharp lower bound on the isoperimetric deficit of a general polygon in terms of the variance of its side lengths, the variance of its radii, and its deviation from being convex. Our technique involves a functional minimization problem on a suitably constructed compact manifold and is based on the spectral theory for circulant matrices.
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。
