Intrinsically quasi-isometric sections in metric spaces

Daniela Di Donato

Intrinsically quasi-isometric sections in metric spaces

Metric Geometry 2022-05-09 v1 Classical Analysis and ODEs Differential Geometry

Authors: Daniela Di Donato

Abstract

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.

Keywords

large scale geometry quasi-isometric sections metric spaces ahlfors-david regularity cheeger theory equivalence relation

Cite

@article{arxiv.2205.03351,
  title  = {Intrinsically quasi-isometric sections in metric spaces},
  author = {Daniela Di Donato},
  journal= {arXiv preprint arXiv:2205.03351},
  year   = {2022}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2205.02688, arXiv:2205.02086

Intrinsically quasi-isometric sections in metric spaces

Abstract

Keywords

Cite

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