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2010 Some Remarks About Parametrizations of Intrinsic Regular Surfaces in the Heisenberg Group
Francesco Bigolin, Davide Vittone
Publ. Mat. 54(1): 159-172 (2010).

Abstract

We prove that, in general, ${\mathbb H}$-regular surfaces in the Heisenberg group $\mathbb{H}^1$ are not bi-Lipschitz equivalent to the plane ${\mathbb R}^2$ endowed with the ``parabolic'' distance, which instead is the model space for $C^1$ surfaces without characteristic points. In Heisenberg groups $\mathbb{H}^n$, ${\mathbb H}$-regular surfaces can be seen as intrinsic graphs: we show that such parametrizations do not belong to Sobolev classes of metric-space valued maps.

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Francesco Bigolin. Davide Vittone. "Some Remarks About Parametrizations of Intrinsic Regular Surfaces in the Heisenberg Group." Publ. Mat. 54 (1) 159 - 172, 2010.

Information

Published: 2010
First available in Project Euclid: 8 January 2010

zbMATH: 1188.53028
MathSciNet: MR2603594

Subjects:
Primary: 53C17 , 54E40

Keywords: ${\mathbb H}$-regular surfaces , Bi-Lipschitz parametrizations , Heisenberg group

Rights: Copyright © 2010 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.54 • No. 1 • 2010
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