Rectifiability and parameterization of intrinsic regular surfaces in the Heisenberg group. (English) Zbl 1170.28300
Summary: We construct an intrinsic regular surface in the first Heisenberg group \(\mathbb{H}^1\equiv\mathbb{R}^3\) 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 \(\tfrac 12\)-Hölder continuous parameterization.
MSC:
| 28A75 | Length, area, volume, other geometric measure theory |
| 28A78 | Hausdorff and packing measures |
| 22E25 | Nilpotent and solvable Lie groups |
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