欧氏与高斯Cheeger常数的定量下界
偏微分方程分析
2023-11-07 v4
摘要
我们针对欧氏与高斯两种情形，借助适当的不对称指数，给出了集合 的 Cheeger 常数的定量下界。我们给出了例子表明这些定量估计是锐利的。
引用
@article{arxiv.2003.10930,
title = {Quantitative lower bounds to the Euclidean and the Gaussian Cheeger constants},
author = {Vesa Julin and Giorgio Saracco},
journal= {arXiv preprint arXiv:2003.10930},
year = {2023}
}
备注
18 pages, 3 figures. In the published paper in the definition (2.2) of the index $\zeta(\Omega)$ the rescaling factor is missing (as otherwise the quantitative inequality (2.5) would be false as written). Consequently, in the proof of Theorem 2.1 and in the following example several renormalization constants are missing. The preprint contains the correct definition and proofs