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SRA-free condition by Zolotov for self-contracted curves and nondegeneracy of the zz-distance for Möbius structures on the circle
St. Petersburg Mathematical Journal ( IF 0.7 ) Pub Date : 2020-09-03 , DOI: 10.1090/spmj/1624
S. Buyalo

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.


中文翻译:

Zolotov对圆上Möbius结构的自收缩曲线和zz距离的简并性的无SRA条件

摘要:Zolotov引入了公制空间(即没有小粗角的空间)的无SRA条件,以研究各种公制空间中自收缩曲线的可校正性。引入了该概念的莫比乌斯不变式,它使人可以证明与圆上相应莫比乌斯结构有关的zz距离是不退化的。该结果是解决圆上Möbius几何反问题的重要部分。
更新日期:2020-09-10
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