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

Abstract

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