Variations of generalized area functionals and p-area minimizers of bounded variation in the Heisenberg group

zbMath1232.35178arXiv1102.2691MaRDI QIDQ3171326

Jih-Hsin Cheng, Jenn-Fang Hwang

Publication date: 5 October 2011

Full work available at URL: https://arxiv.org/abs/1102.2691

zbMATH Keywords

Heisenberg groupminimizerfirst and second variations\(BV\)-functions\(p\)-area

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) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

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Strong maximum principle for mean curvature operators on subRiemannian manifolds ⋮ Existence, characterization and stability of Pansu spheres in sub-Riemannian 3-space forms ⋮ An instability criterion for volume-preserving area-stationary surfaces with singular curves in sub-Riemannian 3-space forms ⋮ First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-Hermitian manifolds ⋮ Variational formulas for submanifolds of fixed degree ⋮ Umbilicity and characterization of Pansu spheres in the Heisenberg group ⋮ The prescribed \(p\)-mean curvature equation of low regularity in the Heisenberg group ⋮ Uniqueness of generalized \(p\)-area minimizers and integrability of a horizontal normal in the Heisenberg group ⋮ Submanifolds of fixed degree in graded manifolds for perceptual completion ⋮ Strongly stable surfaces in sub-Riemannian 3-space forms

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