Calculus of Variations and Geometric Measure Theory

D. Di Donato

Intrinsically quasi-isometric sections in metric spaces

created by didonato on 16 May 2022



Inserted: 16 may 2022
Last Updated: 16 may 2022

Year: 2022

ArXiv: 2205.03351 PDF


This note is a contribution to large scale geometry. More precisely, we introduce the intrinsically quasi-isometric sections in metric spaces and we investigate their properties: the Ahlfors-David regularity in large scale; following Cheeger theory, it is possible to define suitable sets in order to obtain convexity and being a vector space over $\mathbb{R}$ or $\mathbb{C}$ for these sections; yet, following Cheeger's idea, we give an equivalence relation for this class of sections. Throughout the paper, we use basic mathematical tools.