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Pré-Publication, Document De Travail Année : 2022

Classification of uniformly distributed measures of dimension $1$ in general codimension

Résumé

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.

Dates et versions

hal-03869784 , version 1 (24-11-2022)

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Paul Laurain, Mircea Petrache. Classification of uniformly distributed measures of dimension $1$ in general codimension. 2022. ⟨hal-03869784⟩
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