Steiner 公式与等周不等式的变分证明
微分几何
2021-01-15 v3 经典分析与常微分方程
摘要
我们基于 Steiner 关于凸邻域面积的公式，给出了平面中等周不等式的一个新证明。该证明直接建立了等周不等式，无需单独证明最优域的存在性。由此，该证明绕过了 Steiner 为平面等周不等式所概述的所有证明中的主要困难。
关键词
引用
@article{arxiv.1909.06347,
title = {Steiner's formula and a variational proof of the isoperimetric inequality},
author = {Joseph Ansel Hoisington},
journal= {arXiv preprint arXiv:1909.06347},
year = {2021}
}
备注
Comments Welcome! v3 contains a new proof of one of the main lemmas, and a correspondingly simplified proof of the main result. The proof of the characterization of equality in this version also addresses a gap in this part of the proof in v1 and v2