Quantitative bi-Lipschitz embeddings of bounded-curvature manifolds and orbifolds

Sylvester Eriksson‐Bique

Type: Article

Publication Date: 2018-04-05

Citations: 3

DOI: https://doi.org/10.2140/gt.2018.22.1961

Abstract

We construct bi-Lipschitz embeddings into Euclidean space for manifolds and orbifolds of bounded diameter and curvature. The distortion and dimension of such embeddings is bounded by diameter, curvature and dimension alone. Our results also apply for bounded subsets of complete Riemannian manifolds, and complete flat and elliptic orbifolds. Our approach is based on analysing the structure of a bounded curvature manifold at various scales by specializing methods from collapsing theory to a certain class of model spaces.

Locations

arXiv (Cornell University) - View - PDF
Project Euclid (Cornell University) - View - PDF
DataCite API - View
Geometry & Topology - View

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+	Plongements lipschitziens dans Rn	2003	Patrice Assouad
+	Metric Structures for Riemannian and Non-Riemannian Spaces	2007	Mikhael Gromov
+	Three-Dimensional Geometry and Topology	1997	William P. Thurston Silvio Levy
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+	Ultrametric spaces bi-Lipschitz embeddable in $ℝ^n$	1996	Kerkko Luosto
+	A boundary of the set of the Riemannian manifolds with bounded curvatures and diameters	1988	Kenji Fukaya
+ PDF Chat	Surfaces with generalized second fundamental form in $L^2$ are Lipschitz manifolds	1994	Tatiana Toro
+	Geometric conditions and existence of bi-Lipschitz parameterizations	1995	Tatiana Toro