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arXiv · 1411.2512

Wasserstein Distance and the Rectifiability of Doubling Measures: Part II

Jonas Azzam·Guy David·Tatiana Toro
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Abstract

We study the structure of the support of a doubling measure by analyzing its self-similarity properties, which we estimate using a variant of the $L^1$ Wasserstein distance. We show that measure satisfying certain self-similarity conditions admits a unique (up to multiplication by a constant) flat tangent measure at almost every point. This allows us to decompose the support into rectifiable pieces of various dimensions.

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Jonas Azzam, Guy David, Tatiana Toro. 2014-11-10. Wasserstein Distance and the Rectifiability of Doubling Measures: Part II. https://arxiv.org/abs/1411.2512

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