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Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group
We construct an intrinsic regular surface in the first Heisenberg group H 1 ≡ 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 1 2 -Hölder continuous parameterization.