Calculus of Variations and Geometric Measure Theory
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B. Kirchheim - F. Serra Cassano

Rectifiability and parametrization of intrinsic regular surfaces in the Heisenberg group

created on 19 Dec 2003
modified by serracas on 18 Dec 2006


Published Paper

Inserted: 19 dec 2003
Last Updated: 18 dec 2006

Journal: Ann. Scuola Norm.Sup. Pisa Cl.Sci. (5)
Volume: III
Pages: 871-896
Year: 2004


We construct an intrinsic regular surface in the first Heisenberg group $\mathbb H^1=\mathbb R^3$ equipped wiht its Carnot- Carathéodory metric which has Euclidean Hausdorff dimension $2.5$. Moreover we prove that each intrinsic regular surface in this setting is a $2$- dimensional topological manifold admitting a $\frac{1}{2}$- Hölder continuous parametrization.

Keywords: Carnot groups, intrinsic regular surfaces and classical rectifiability, parametrization of surfaces, Hölder continuos functions


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