A Selection Principle for the Sharp Quantitative Isoperimetric Inequality
A Selection Principle for the Sharp Quantitative Isoperimetric Inequality
复制标题
DOI：
10.1007/s00205-012-0544-1
复制
发表时间：
2010-07
影响因子：
2.5
通讯作者：
M. Cicalese;G. P. Leonardi
中科院分区：
文献类型：
--
作者：
M. Cicalese;G. P. Leonardi
本文引入了一种新的变分方法来研究等距定量不等式。该方法基于惩罚技术和周长拟极小值的正则性理论，具有通用性。提出了两个值得注意的应用。首先给出了中尖锐定量等周不等式的一个新的证明。其次，我们肯定地回答了霍尔关于小不对称区域中定量等周不等式的最佳常数的猜想。
We introduce a new variational method for the study of isoperimetric inequalities with quantitative terms. The method is general as it relies on a penalization technique combined with the regularity theory for quasiminimizers of the perimeter. Two notable applications are presented. First we give a new proof of the sharp quantitative isoperimetric inequality in. Second we positively answer a conjecture by Hall concerning the best constant for the quantitative isoperimetric inequality inin the small asymmetry regime.