scholarly journals Global Lipschitz extension preserving local constants

2021 ◽  
Vol 31 (4) ◽  
pp. 757-765
Author(s):  
Simone Di Marino ◽  
Nicola Gigli ◽  
Aldo Pratelli
Keyword(s):  
Lipschitz Extension

scholarly journals Sobolev Extensions of Lipschitz Mappings into Metric Spaces

2017 ◽  
Vol 2019 (8) ◽  
pp. 2241-2265
Author(s):  
Scott Zimmerman
Keyword(s):  
Heisenberg Group ◽  
Bounded Domain ◽  
Compact Subset ◽  
Metric Space ◽  
Metric Spaces ◽  
Extension Property ◽  
Lipschitz Mapping ◽  
Lipschitz Extension ◽  
Lipschitz Mappings ◽  
Lipschitz Map

Abstract Wenger and Young proved that the pair $(\mathbb{R}^m,\mathbb{H}^n)$ has the Lipschitz extension property for $m \leq n$ where $\mathbb{H}^n$ is the sub-Riemannian Heisenberg group. That is, for some $C>0$, any $L$-Lipschitz map from a subset of $\mathbb{R}^m$ into $\mathbb{H}^n$ can be extended to a $CL$-Lipschitz mapping on $\mathbb{R}^m$. In this article, we construct Sobolev extensions of such Lipschitz mappings with no restriction on the dimension $m$. We prove that any Lipschitz mapping from a compact subset of $\mathbb{R}^m$ into $\mathbb{H}^n$ may be extended to a Sobolev mapping on any bounded domain containing the set. More generally, we prove this result in the case of mappings into any Lipschitz $(n-1)$-connected metric space.

scholarly journals Efficient Regression in Metric Spaces via Approximate Lipschitz Extension

2017 ◽  
Vol 63 (8) ◽  
pp. 4838-4849 ◽  
Author(s):  
Lee-Ad Gottlieb ◽  
Aryeh Kontorovich ◽  
Robert Krauthgamer
Keyword(s):  
Metric Spaces ◽  
Lipschitz Extension

scholarly journals A planar bi-Lipschitz extension theorem

2015 ◽  
Vol 8 (3) ◽  
Author(s):  
Sara Daneri ◽  
Aldo Pratelli
Keyword(s):  
Extension Theorem ◽  
Lipschitz Extension ◽  
Lipschitz Map

AbstractWe prove that, given a planar bi-Lipschitz map

scholarly journals Absolutely minimal Lipschitz extension of tree-valued mappings

2011 ◽  
Vol 354 (3) ◽  
pp. 1049-1078 ◽  
Author(s):  
Assaf Naor ◽  
Scott Sheffield
Keyword(s):  
Lipschitz Extension

scholarly journals Spectral Calculus and Lipschitz Extension for Barycentric Metric Spaces

2013 ◽  
Vol 1 ◽  
pp. 163-199 ◽  
Author(s):  
Manor Mendel ◽  
Assaf Naor
Keyword(s):  
Banach Spaces ◽  
Metric Spaces ◽  
Extension Theorem ◽  
Unified Framework ◽  
Lipschitz Extension

Abstract The metric Markov cotype of barycentric metric spaces is computed, yielding the first class of metric spaces that are not Banach spaces for which this bi-Lipschitz invariant is understood. It is shown that this leads to new nonlinear spectral calculus inequalities, as well as a unified framework for Lipschitz extension, including new Lipschitz extension results for CAT (0) targets. An example that elucidates the relation between metric Markov cotype and Rademacher cotype is analyzed, showing that a classical Lipschitz extension theorem of Johnson, Lindenstrauss and Benyamini is asymptotically sharp.

Sign in / Sign up

Export Citation Format

Share Document