We construct an intrinsic regular surface in the first Heisenberg group H-1 drop R-3 equipped wiht its Carnot-Caratheodory 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-Holder continuous parameterization.
Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group
Serra Cassano, Francesco
2004-01-01
Abstract
We construct an intrinsic regular surface in the first Heisenberg group H-1 drop R-3 equipped wiht its Carnot-Caratheodory 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-Holder continuous parameterization.File in questo prodotto:
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