SRA-free condition by Zolotov for self-contracted curves and nondegeneracy of zz-distance for M\"obius 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 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.