各向异性高斯等周不等式和艾哈德对称性

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS ACS Applied Bio Materials Pub Date : 2024-09-09 DOI:10.1007/s00526-024-02818-1

Kuan-Ting Yeh

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引用次数: 0

摘要

在本文中，我们证明了各向异性高斯度量的等周不等式，并描述了相等的情况。我们还找到了一个例子，表明各向异性高斯周长的艾哈德对称性不能减小，并给出了一个包含误差项的新不等式。这个新不等式尤其为我们证明各向异性艾哈德对称性的唯一性结果提供了提示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The anisotropic Gaussian isoperimetric inequality and Ehrhard symmetrization

In this paper, we prove the isoperimetric inequality for the anisotropic Gaussian measure and characterize the cases of equality. We also find an example that shows Ehrhard symmetrization fails to decrease for the anisotropic Gaussian perimeter and gives a new inequality that includes an error term. This new inequality, in particular, gives us a hint to prove a uniqueness result for the anisotropic Ehrhard symmetrization.

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来源期刊

ACS Applied Bio Materials Chemistry-Chemistry (all)

CiteScore

9.40

自引率

2.10%

发文量

464