Nonexistence of horizontal Sobolev surfaces in the Heisenberg group

DOI10.1090/S0002-9939-09-10211-3zbMath1204.53026arXiv0903.2214MaRDI QIDQ3559009

Valentino Magnani

Publication date: 11 May 2010

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.2214

zbMATH Keywords

Heisenberg groupHausdorff measurerectifiable set

Mathematics Subject Classification ID

Hausdorff and packing measures (28A78) Sub-Riemannian geometry (53C17) Functions of several variables (26B99)

Related Items (1)

A low rank property and nonexistence of higher-dimensional horizontal Sobolev sets

Cites Work

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• Sobolev Peano cubes
• Comparison of Hausdorff measures with respect to the Euclidean and the Heisenberg metric
• Rectifiable sets in metric and Banach spaces
• Change of variables formula under minimal assumptions
• Size of characteristic sets and functions with prescribed gradient
• The co-area formula for Sobolev mappings
• Lifts of Lipschitz maps and horizontal fractals in the Heisenberg group
• Contact equations, Lipschitz extensions and isoperimetric inequalities

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