This article is cited in 17 papers

Linear bilipschitz extension property

P. Alestalo^a, D. A. Trotsenko^b, J. Vyaisyalya<sup>c

a</sup> Helsinki University of Technology
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^c University of Helsinki

Abstract: We give a sufficient geometric condition for a subset $A$ of $\mathbb{R}^n$ to enjoy the following property for a fixed $C\geqslant1$ There is $\delta>0$ such that for $0\leqslant\varepsilon\leqslant\delta$, each $(1+\varepsilon)$-bilipschitz map $f\colon A\to\mathbb{R}^n$ extends to a $(1+C\varepsilon)$-bilipschitz map $F\colon\mathbb{R}^n\to\mathbb{R}^n$.

Keywords: bilipschitz mapping, quasi-isometry, approximation, extension of mappings, subsets of euclidean space.

UDC: 517.548.2

Received: 27.06.2003

 English version: Siberian Mathematical Journal, 2003, 44:6, 959–968

Bibliographic databases:

• 
• 
•