S. V. Buyalo, “SRA-free condition by Zolotov for self-contracted curves and nondegeneracy of the zz-distance for Möbius structures on the circle”, Algebra i Analiz, 2019, Volume 31, Issue 5,Pages <nobr>90

Research Papers

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

S. V. Buyalo

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: The SRA-free condition for metric spaces (that is, spaces without Small Rough Angles) was introduced by Zolotov to study rectifiability for self-contracted curves in various metric spaces. A Möbius invariant version of this notion is introduced, which allows one to show that the zz-distance associated with the 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.

Keywords: Möbius structures, cross-ratio, harmonic 4-tuples, self-contracted curves.

MSC: 51B10

Received: 25.06.2019