Abstract In this paper, we introduce the notion of local quasi-isometry for metric germs and prove that two definable germs are quasi-isometric if and only if their tangent cones are bi-Lipschitz homeomorphic. Since bi-Lipschitz equivalence is a particular case of local quasi-isometric equivalence, we obtain Sampaio’s tangent cone theorem as a corollary. As an application, we provide a different proof of the theorem by Fernandes-Sampaio, which states that the tangent cone of a Lipschitz normally embedded germ is also Lipschitz normally embedded.

Nhan Nguyen

Advances in Geometry

ADVANCES IN GEOMETRY 是一本数学期刊，用于发表几何领域中质量卓越的原创研究文章。几何学是一个具有悠久传统和显着重要性的领域。空间和空间模式的研究是一项主要的数学活动；几何思想和几何语言渗透到所有的数学中。

Advances in Geometry is a mathematics journal dedicated to publishing high-quality original research articles in the field of geometry. Geometry, with its long-standing tradition and significant importance, involves the study of space and spatial patterns, which is a major mathematical activity. Geometric ideas and language permeate all areas of mathematics.

《Advances in Geometry》是一本专注于几何领域的数学期刊，致力于发表高质量的原创研究文章。几何学作为一个历史悠久且极具重要性的学科，涉及空间及其模式的研究，这是一项主要的数学活动。几何思想和语言在所有数学领域中都有着深刻的影响。

Category	Quartile
数学	4
数学, 数学	4

Local quasi-isometries and tangent cones of definable germs

ivySCI AI Smartly Parses PDF, Answers Researchers' Questions, and Helps You Understand Papers in Seconds

Journal Info