豪斯多夫度量和里兹容量衰减率

arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-09-04 DOI:arxiv-2409.03070

Qiuling Fan, Richard S. Laugesen

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引用次数: 0

摘要

随着指数增加到集合的维数，里兹容量的衰减率会产生豪斯多夫度量。这一结果适用于强可校正集合，因此尤其适用于欧几里得空间的子实体。对于严格自相似的分形，找到了单边衰减估计。在此过程中，还给出了关于里兹能量倒数的次等性的纯度量理论证明。

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Hausdorff measure and decay rate of Riesz capacity

The decay rate of Riesz capacity as the exponent increases to the dimension of the set is shown to yield Hausdorff measure. The result applies to strongly rectifiable sets, and so in particular to submanifolds of Euclidean space. For strictly self-similar fractals, a one-sided decay estimate is found. Along the way, a purely measure theoretic proof is given for subadditivity of the reciprocal of Riesz energy.

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arXiv - MATH - Classical Analysis and ODEs

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