Bi-Lipschitz embeddings of Heisenberg submanifolds into Euclidean spaces

DOI10.5186/aasfm.2020.4551zbMath1450.30076arXiv1812.07612OpenAlexW3034998252WikidataQ114019224 ScholiaQ114019224MaRDI QIDQ5118938

Vasileios Chousionis, Scott Zimmerman, Vyron Vellis, Sean Li

Publication date: 27 August 2020

Published in: Annales Academiae Scientiarum Fennicae Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.07612

zbMATH Keywords

Heisenberg groupbi-Lipschitz embeddingporous sets

Mathematics Subject Classification ID

Sub-Riemannian geometry (53C17) Geometric embeddings of metric spaces (30L05)

Cites Work

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• Markov convexity and nonembeddability of the Heisenberg group
• An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• Bi-Lipschitz embedding of the generalized Grushin plane into Euclidean spaces
• Structure of porous sets in Carnot groups
• Smooth quasiregular mappings with branching
• On the nonexistence of bilipschitz parameterizations and geometric problems about \(A_ \infty\)-weights
• A characterization of bi-Lipschitz embeddable metric spaces in terms of local bi-Lipschitz embeddability
• Porosity, differentiability and Pansu's theorem
• Conformal Grushin spaces
• Bilipschitz Embedding of Grushin Plane in R^3
• L_1 embeddings of the Heisenberg group and fast estimation of graph isoperimetry
• Plongements lipschitziens dans ${\bbfR}\sp n$
• Size of characteristic sets and functions with prescribed gradient
• The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative-Type Metrics into ℓ ₁
• Bilipschitz embeddings of metric spaces into space forms