Properly embedded and immersed minimal surfaces in the Heisenberg group

DOI10.1017/S0004972700034766zbMath1062.35046arXivmath/0407094OpenAlexW2010379136WikidataQ125907770 ScholiaQ125907770MaRDI QIDQ3158790

Jenn-Fang Hwang, Jih-Hsin Cheng

Publication date: 31 January 2005

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0407094

zbMATH Keywords

3-dimensional Heisenberg groupannulus typeband typehelicoid type \(p\)-minimal surfaces

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Degenerate elliptic equations (35J70) Optimization of shapes other than minimal surfaces (49Q10) Degenerate hyperbolic equations (35L80) Analysis on CR manifolds (32V20)

Related Items

Strong maximum principle for mean curvature operators on subRiemannian manifolds, A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group, Regularity for subelliptic PDE through uniform estimates in multi-scale geometries, Convex hull property and exclosure theorems for \(H\)-minimal hypersurfaces in Carnot groups, Sub-Riemannian calculus on hypersurfaces in Carnot groups, The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations, Existence and uniqueness for \(p\)-area minimizers in the Heisenberg group, Unnamed Item, Intrinsic curvature of curves and surfaces and a Gauss-Bonnet theorem in the Heisenberg group, Existence, characterization and stability of Pansu spheres in sub-Riemannian 3-space forms, Free boundary constant p-mean curvature surfaces intersecting the Pansu sphere, An intrinsic measure for submanifolds in stratified groups, Complete stable CMC surfaces with empty singular set in Sasakian sub-Riemannian 3-manifolds, Area-stationary surfaces in the Heisenberg group \(\mathbb H^1\), Umbilicity and characterization of Pansu spheres in the Heisenberg group, The graphs of Lipschitz functions and minimal surfaces on Carnot groups, The classification of complete stable area-stationary surfaces in the Heisenberg group, Sub-Riemannian calculus and monotonicity of the perimeter for graphical strips, The prescribed \(p\)-mean curvature equation of low regularity in the Heisenberg group, Minimal surfaces in the roto-translation group with applications to a neuro-biological image completion model, Rotationally invariant hypersurfaces with constant mean curvature in the Heisenberg group \(\mathbb H^n\), Uniqueness of generalized \(p\)-area minimizers and integrability of a horizontal normal in the Heisenberg group, A partial solution of the isoperimetric problem for the Heisenberg group, Examples of area-minimizing surfaces in the sub-Riemannian Heisenberg group \({\mathbb{H}^1}\) with low regularity, Regularity of \(C^{1}\) smooth surfaces with prescribed \(p\)-mean curvature in the Heisenberg group, Minimal surfaces in sub-Riemannian manifolds and structure of their singular sets in the(2,3)case, Affine biharmonic submanifolds in 3-dimensional pseudo-Hermitian geometry, Existence and structure of \(P\)-area minimizing surfaces in the Heisenberg group, Strongly stable surfaces in sub-Riemannian 3-space forms

Cites Work

• Unnamed Item
• Topology and curvature of minimal surfaces properly embedded in \(\mathbb{R}^ 3\)
• The strong halfspace theorem for minimal surfaces
• Minimal surfaces in the Heisenberg group
• Example of a complete minimal immersion in IR3 of genus one and three-embedded ends
• Complete embedded minimal surfaces of finite total curvature