Rotationally invariant hypersurfaces with constant mean curvature in the Heisenberg group \(\mathbb H^n\)
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Publication:2508673
DOI10.1007/BF02922137zbMath1129.53041arXivmath/0504439MaRDI QIDQ2508673
Publication date: 20 October 2006
Published in: The Journal of Geometric Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0504439
Differential geometry of homogeneous manifolds (53C30) Variational problems in a geometric measure-theoretic setting (49Q20) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Sub-Riemannian geometry (53C17)
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Cites Work
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- The structure of complete embedded surfaces with constant mean curvature
- Constant mean curvature surfaces in sub-Riemannian geometry
- Stability of hypersurfaces of constant mean curvature in Riemannian manifolds
- Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
- On generalization of theorems of A. D. Alexandrov and C. Delaunay on hypersurfaces of constant mean curvature
- Invariant surfaces of the Heisenberg groups
- Minimal surfaces in the Heisenberg group
- The geometric Sobolev embedding for vector fields and the isoperimetric inequality
- On the isoperimetric problem in the Heisenberg group \(\mathbb H^n\)
- Sub-Riemannian constant mean curvature surfaces in the Heisenberg group as limits
- Properly embedded and immersed minimal surfaces in the Heisenberg group
- Size of characteristic sets and functions with prescribed gradient
- Rectifiability and perimeter in the Heisenberg group
- Surface measures in Carnot-Carathéodory spaces
- Sur un théorème de traces. (On a trace theorem)
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