Hypersurfaces and variational formulas in sub-Riemannian Carnot groups

DOI10.1016/j.matpur.2007.01.009zbMath1123.49035arXiv1012.2442OpenAlexW1978321143WikidataQ115343601 ScholiaQ115343601MaRDI QIDQ884002

Francescopaolo Montefalcone

Publication date: 13 June 2007

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.2442

zbMATH Keywords

hypersurfacessub-Riemannian geometryCarnot groupsfirst variation of the \(H\)-perimetersecond variation of the \(H\)-perimeter

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Lie algebras of Lie groups (22E60)

Related Items

The weighted isoperimetric-type and Sobolev-type inequalities for hypersurfaces in Carnot groups, Convex hull property and exclosure theorems for \(H\)-minimal hypersurfaces in Carnot groups, Sub-Riemannian calculus on hypersurfaces in Carnot groups, First variation of the Hausdorff measure of non-horizontal submanifolds in sub-Riemannian stratified Lie groups, 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, First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-Hermitian manifolds, Intrinsic complements of equiregular sub-Riemannian manifolds, Complete stable CMC surfaces with empty singular set in Sasakian sub-Riemannian 3-manifolds, Variational formulas for submanifolds of fixed degree, Sub-Riemannian calculus and monotonicity of the perimeter for graphical strips, An integral formula on the Heisenberg group, Collapsing Riemannian Metrics to Sub-Riemannian and the Geometry of Hypersurfaces in Carnot Groups, Regularity of minimal intrinsic graphs in 3-dimensional sub-Riemannian structures of step 2, Stable \(H\)-minimal hypersurfaces, Strongly stable surfaces in sub-Riemannian 3-space forms

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