Calculus of Variations and Geometric Measure Theory
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E. Le Donne

Properties of isometrically homogeneous curves

created by ledonne on 21 Dec 2018

[BibTeX]

preprint

Inserted: 21 dec 2018

Year: 2011

ArXiv: 1108.5830 PDF

Abstract:

This paper is devoted to the study of isometrically homogeneous spaces from the view point of metric geometry. Mainly we focus on those spaces that are homeomorphic to lines. One can reduce the study to those distances on $\R$ that are translation invariant. We study possible values of various metric dimensions of such spaces. One of the main results is the equivalence of two properties: the first one is linear connectedness and the second one is 1-dimensionality, with respect to Nagata dimension. Several concrete pathological examples are provided.

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