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

Abstract:

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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