非坍缩RCD度量空间中定量奇异地层的体积边界

Pub Date : 2019-01-01 DOI:10.1515/agms-2019-0008

Gioacchino Antonelli, Elia Brué, Daniele Semola

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引用次数: 16

摘要

摘要本文的目的是将Cheeger和Naber在[13]中为非坍缩Ricci极限获得的有效奇异地层的体积界推广到非坍缩RCD（K，N）度量测度空间类。这一证明是基于定量微分的论点，与最初的论点密切相关。作为一个简单的结果，我们为ncRCD（K，N）空间的Gigli-DePhilippis边界（[20，备注3.8]）的扩大提供了一个体积估计。

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Volume Bounds for the Quantitative Singular Strata of Non Collapsed RCD Metric Measure Spaces

Abstract The aim of this note is to generalize to the class of non collapsed RCD(K, N) metric measure spaces the volume bound for the effective singular strata obtained by Cheeger and Naber for non collapsed Ricci limits in [13]. The proof, which is based on a quantitative differentiation argument, closely follows the original one. As a simple outcome we provide a volume estimate for the enlargement of Gigli-DePhilippis’ boundary ([20, Remark 3.8]) of ncRCD(K, N) spaces.

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