Classification of uniformly distributed measures of dimension $1$ in general codimension
| Autor: | Laurain, P., Petrache, M. |
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| Rok vydání: | 2019 |
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| Zdroj: | Asian Journal of Mathematics |
| DOI: | 10.48550/arxiv.1905.09601 |
| Popis: | Starting with the work of Preiss on the geometry of measures, the classification of uniform measures in $\mathbb R^d$ has remained open, except for $d=1$ and for compactly supported measures in $d=2$, and for codimension $1$. In this paper we study $1$-dimensional measures in $\mathbb R^d$ for all $d$ and classify uniform measures with connected $1$-dimensional support, which turn out to be homogeneous measures. We provide as well a partial classification of general uniform measures of dimension $1$ in the absence of the connected support hypothesis. Comment: 12 pages |
| Databáze: | OpenAIRE |
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