First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-Hermitian manifolds

DOI10.1007/S00526-012-0513-4zbMath1268.53039arXiv1109.6213OpenAlexW2072268718WikidataQ115387494 ScholiaQ115387494MaRDI QIDQ1949407

Matteo Galli

Publication date: 7 May 2013

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.6213

zbMATH Keywords

second variationsingular setWebster scalar curvaturepseudo-Hermitian manifoldspseudo-Hermitian torsion

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Sub-Riemannian geometry (53C17)

Related Items (15)

The regularity of Euclidean Lipschitz boundaries with prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds ⋮ Area-stationary and stable surfaces of class \(C^1\) in the sub-Riemannian Heisenberg group \(\mathbb{H}^1\) ⋮ Regularity of \(C^1\) surfaces with prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds ⋮ Existence, characterization and stability of Pansu spheres in sub-Riemannian 3-space forms ⋮ Second variation of sub-Riemannian surface measure of non-horizontal submanifolds in sub-Riemannian stratified Lie groups ⋮ Free boundary constant p-mean curvature surfaces intersecting the Pansu sphere ⋮ Area-minimizing horizontal graphs with low regularity in the sub-Finsler Heisenberg group \({\mathbb{H}}^1\) ⋮ An instability criterion for volume-preserving area-stationary surfaces with singular curves in sub-Riemannian 3-space forms ⋮ Some remarks on contact variations in the first Heisenberg group ⋮ Unnamed Item ⋮ Tubular neighborhoods in the sub-Riemannian Heisenberg groups ⋮ Complete stable CMC surfaces with empty singular set in Sasakian sub-Riemannian 3-manifolds ⋮ Variational formulas for submanifolds of fixed degree ⋮ Stable \(H\)-minimal hypersurfaces ⋮ Strongly stable surfaces in sub-Riemannian 3-space forms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Complete stable CMC surfaces with empty singular set in Sasakian sub-Riemannian 3-manifolds
• On contact manifolds
• Intrinsic regular hypersurfaces in Heisenberg groups
• A cortical based model of perceptual completion in the roto-translation space
• An introduction to the Heisenberg group and the sub-Riemannian isoperimetric problem
• Existence and uniqueness for \(p\)-area minimizers in the Heisenberg group
• Regular submanifolds, graphs and area formula in Heisenberg groups
• Hypersurfaces and variational formulas in sub-Riemannian Carnot groups
• Constant mean curvature surfaces in sub-Riemannian geometry
• The symplectic structure of the primary visual cortex
• Area-stationary surfaces in the Heisenberg group \(\mathbb H^1\)
• The classification of complete stable area-stationary surfaces in the Heisenberg group
• Instability of graphical strips and a positive answer to the Bernstein problem in the Heisenberg group \(\mathbb H^1\)
• Examples of area-minimizing surfaces in the sub-Riemannian Heisenberg group \({\mathbb{H}^1}\) with low regularity
• Homogeneous contact Riemannian three-manifolds
• Differential forms on contact manifolds
• Existence of isoperimetric regions in contact sub-Riemannian manifolds
• Differential geometry and analysis on CR manifolds
• Sub-Riemannian calculus on hypersurfaces in Carnot groups
• Regular hypersurfaces, intrinsic perimeter and implicit function theorem in Carnot groups
• Area-stationary surfaces inside the sub-Riemannian three-sphere
• The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations
• A Codazzi-like equation and the singular set for C1 smooth surfaces in the Heisenberg group
• Variations of generalized area functionals and p-area minimizers of bounded variation in the Heisenberg group
• Isoperimetric inequalities & volume comparison theorems on CR manifolds
• A notable family of entire intrinsic minimal graphs in the Heisenberg group which are not perimeter minimizing
• Minimal surfaces in sub-Riemannian manifolds and structure of their singular sets in the(2,3)case
• Variational Problems on Contact Riemannian Manifolds
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• Riemannian geometry of contact and symplectic manifolds
• Rectifiability and perimeter in the Heisenberg group

This page was built for publication: First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-Hermitian manifolds