SRA-free condition by Zolotov for self-contracted curves and nondegeneracy of zz-distance for Möbius structures on the circle

2019/06/21 by Sergei Buyalo, Buyalo, Sergei
Mathematics · #51B10 #FOS: Mathematics #Metric Geometry (math.MG) #math.MG #msc:51B10

paper · pdf · doi:10.48550/arxiv.1906.09966

15 pages. arXiv admin note: text overlap with arXiv:1810.03133

arxiv created 2019/06/21 · arxiv updated 2019/06/25

Abstract

SRA-free condition for metric spaces (that is, spaces without Small Rough Angles) was introduced by Zolotov to study rectifiability of self-contracted curves in various metric spaces. We give a Moebius invariant version of this notion which allows to show that zz-distance associated with a respective Moebius structure on the circle is nondegenerate. This result is an important part of a solution to the inverse problem of Moebius geometry on the circle.

Citations

• On the inverse problem of Moebius geometry on the circle

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