Sub-Riemannian calculus on hypersurfaces in Carnot groups

DOI10.1016/j.aim.2007.04.004zbMath1129.53017arXivmath/0607559OpenAlexW2126918903WikidataQ115362122 ScholiaQ115362122MaRDI QIDQ2381964

Donatella Danielli, Nicola Garofalo, Duy-Minh Nhieu

Publication date: 26 September 2007

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607559

zbMATH Keywords

integration by parts\(H\)-mean curvaturefirst and second variation of the horizontal perimeterhorizontal Lévi-Civita connectionhorizontal second fundamental form

Mathematics Subject Classification ID

Nilpotent and solvable Lie groups (22E25) Sub-Riemannian geometry (53C17)

Related Items

Integrability of the sub-Riemannian mean curvature of surfaces in the Heisenberg group, The weighted isoperimetric-type and Sobolev-type inequalities for hypersurfaces in Carnot groups, The regularity of Euclidean Lipschitz boundaries with prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds, The first eigenvalue of the Kohn-Laplace operator 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, Gauss-Bonnet theorem in sub-Riemannian Heisenberg space \(\mathbb H^1\), Conformal maps of Carnot groups, Inequalities and bounds for the eigenvalues of the sub-Laplacian on a strictly pseudoconvex CR manifold, Heat content asymptotics for sub-Riemannian manifolds, First variation of the Hausdorff measure of non-horizontal submanifolds in sub-Riemannian stratified Lie groups, Hypersurfaces and variational formulas in sub-Riemannian Carnot groups, 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, Integrability of the sub-Riemannian mean curvature at degenerate characteristic points in the Heisenberg group, Intrinsic sub-Laplacian for hypersurface in a contact sub-Riemannian manifold, Second variation of sub-Riemannian surface measure of non-horizontal submanifolds in sub-Riemannian stratified Lie groups, Subelliptic geometric Hardy type inequalities on half-spaces and convex domains, Free boundary constant p-mean curvature surfaces intersecting the Pansu sphere, Compact embeddings, eigenvalue problems, and subelliptic Brezis-Nirenberg equations involving singularity on stratified Lie groups, Surfaces of genus g ≥ 1 in 3D contact sub-Riemannian manifolds, First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-Hermitian manifolds, Complete stable CMC surfaces with empty singular set in Sasakian sub-Riemannian 3-manifolds, Regularity of Lipschitz boundaries with prescribed sub-Finsler mean curvature in the Heisenberg group \(\mathbb{H}^1\), Regularity of mean curvature flow of graphs on Lie groups free up to step 2, Area-stationary surfaces in the Heisenberg group \(\mathbb H^1\), Area-stationary surfaces inside the sub-Riemannian three-sphere, Variational formulas for submanifolds of fixed degree, Geometric second derivative estimates in Carnot groups and convexity, Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups, Sub-Riemannian Geometry and Hypoelliptic Operators, Convexity and horizontal second fundamental forms for hypersurfaces in 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, An integral formula on the Heisenberg group, Blow-up estimates at horizontal points and applications, Collapsing Riemannian Metrics to Sub-Riemannian and the Geometry of Hypersurfaces in Carnot Groups, Capacity of a condenser in the Heisenberg group, Regularity of minimal intrinsic graphs in 3-dimensional sub-Riemannian structures of step 2, Minimal surfaces in the roto-translation group with applications to a neuro-biological image completion model, Sub-Riemannian Mean Curvature Flow for Image Processing, Elements of potential theory on Carnot groups, Non-horizontal submanifolds and coarea formula, Examples of area-minimizing surfaces in the sub-Riemannian Heisenberg group \({\mathbb{H}^1}\) with low regularity, Smoothness of Lipschitz minimal intrinsic graphs in Heisenberg groups , n > 1, Properties of a frequency of Almgren type for harmonic functions in Carnot groups, On viscosity and equivalent notions of solutions for anisotropic geometric equations, Generalized Mean Curvature Flow in Carnot Groups, Gaffney-Friedrichs inequality for differential forms on Heisenberg groups, Uniqueness of Viscosity Mean Curvature Flow Solution in Two Sub-Riemannian Structures, Unnamed Item, Stable \(H\)-minimal hypersurfaces, Generalized pseudohermitian manifolds, On the induced geometry on surfaces in 3D contact sub-Riemannian manifolds, On transversal submanifolds and their measure, Submanifolds of fixed degree in graded manifolds for perceptual completion, Strongly stable surfaces in sub-Riemannian 3-space forms

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