On the lack of density of Lipschitz mappings in Sobolev spaces with Heisenberg target

DOI10.1090/S1088-4173-2014-00267-7zbMath1316.46034arXiv1109.4641MaRDI QIDQ2922925

Noel DeJarnette, Anton Lukyanenko, Jeremy T. Tyson, Piotr Hajłasz

Publication date: 15 October 2014

Published in: Conformal Geometry and Dynamics of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.4641

zbMATH Keywords

Sobolev spaceHeisenberg groupdensitycompact Riemannian manifoldLipschitz map

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Spaces of vector- and operator-valued functions (46E40) Absolutely continuous real functions of several variables, functions of bounded variation (26B30) Sub-Riemannian geometry (53C17) Homotopy groups of spheres (55Q40) Analysis on metric spaces (30L99) Homotopy groups of special types (55Q70)

Related Items (14)

Partial regularity for holonomic minimisers of quasiconvex functionals ⋮ Lipschitz homotopy groups of contact 3-manifolds ⋮ Asymptotic cones of HNN extensions and amalgamated products. ⋮ Lipschitz mappings, metric differentiability, and factorization through metric trees ⋮ Lipschitz means and mixers on metric spaces ⋮ Homotopy groups of spheres and Lipschitz homotopy groups of Heisenberg groups ⋮ Lipschitz homotopy groups of the Heisenberg groups ⋮ BiLipschitz embeddings of spheres into jet space Carnot groups not admitting Lipschitz extensions ⋮ A low rank property and nonexistence of higher-dimensional horizontal Sobolev sets ⋮ The Whitney extension theorem for \(C^1\), horizontal curves in the Heisenberg group ⋮ The homeomorphism problem for closed 3-manifolds ⋮ Conformal Grushin spaces ⋮ Hölder-topology of the Heisenberg group ⋮ The (𝑛+1)-Lipschitz homotopy group of the Heisenberg group ℍⁿ

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