具有密度的星团的最小周长公式

Rendiconti del Seminario Matematico della Università di Padova Pub Date : 2023-03-17 DOI:10.4171/rsmup/120

Vincenzo Scattaglia

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引用次数: 2

摘要

研究双密度欧几里得空间中簇的等周问题。特别地，我们证明了具有体积V的簇的等周最小化序列的极限对于其自身的体积(可能小于V)总是等周的。特别是，如果它严格小于V，我们提供了一个显式公式。数学学科分类(2020)。主:49 q10。次级:49Q20, 58B20

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A formula for the minimal perimeter of clusters with density

This paper deals with the isoperimetric problem for clusters in a Euclidean space with double density. In particular, we show that a limit of an isoperimetric minimizing sequence of clusters with volumes V is always isoperimetric for its own volumes (which may be smaller than V). In particular, if it is strictly smaller, we provide an explicit formula. Mathematics Subject Classification (2020). Primary: 49Q10. Secondary: 49Q20, 58B20

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Rendiconti del Seminario Matematico della Università di Padova

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