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


2018 ◽  
Vol 20 ◽  
pp. 02010
Author(s):  
Thanh Viet Phan

The classical Lipschitz extension problem in concerned for conditions on a pair of metric spaces (X,dX) and (Y,dY) such that for all Ω ⊂ X and for all Lipschitz function and for all Lipschitz function f : Ω → Y, then there is a function g : X → Y that extends f and has the same Lipschitz constant as f . In this paper we discuss some results and open questions related to that issue.



2017 ◽  
Vol 2019 (8) ◽  
pp. 2241-2265
Author(s):  
Scott Zimmerman

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.



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


2017 ◽  
Vol 219 (1) ◽  
pp. 115-161 ◽  
Author(s):  
Assaf Naor ◽  
Yuval Rabani
Keyword(s):  


2015 ◽  
Vol 8 (3) ◽  
Author(s):  
Sara Daneri ◽  
Aldo Pratelli

AbstractWe prove that, given a planar bi-Lipschitz map



2013 ◽  
Vol 1 ◽  
pp. 163-199 ◽  
Author(s):  
Manor Mendel ◽  
Assaf Naor

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.





2012 ◽  
Vol 164 (1) ◽  
pp. 47-71
Author(s):  
Anton Lukyanenko


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