瓦瑟斯坦空间的几何研究:欧几里得空间

IF 1.2 2区数学 Q1 MATHEMATICS

Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze Pub Date : 2008-04-22 DOI:10.2422/2036-2145.2010.2.03

Benoît R. Kloeckner

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引用次数: 63

摘要

我们研究了欧几里得空间的Wasserstein空间(代价为二次元)作为一个内在度量空间。特别地，我们计算它们的等距群。令人惊讶的是，在这行中，存在一个(唯一的)“奇异的”等距流。这与高维欧几里得空间形成对比，在高维欧几里得空间中，沃瑟斯坦空间的所有等距都保持了度量的形状。我们还研究了这些空间的曲率和各种秩。

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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A geometric study of Wasserstein spaces: Euclidean spaces

We study the Wasserstein space (with quadratic cost) of Euclidean spaces as an intrinsic metric space. In particular we compute their isometry groups. Surprisingly, in the case of the line, there exists a (unique) ``exotic'' isometric flow. This contrasts with the case of higher-dimensional Euclidean spaces, where all isometries of the Wasserstein space preserve the shape of measures. We also study the curvature and various ranks of these spaces.

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来源期刊

Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze 数学-数学

CiteScore

2.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Annals of the Normale Superiore di Pisa, Science Class, publishes papers that contribute to the development of Mathematics both from the theoretical and the applied point of view. Research papers or papers of expository type are considered for publication. The Annals of the Normale Scuola di Pisa - Science Class is published quarterly Soft cover, 17x24