Intrinsic regular hypersurfaces in Heisenberg groups

DOI10.1007/BF02922114zbMath1085.49045OpenAlexW2102561219MaRDI QIDQ819253

Luigi Ambrosio, Davide Vittone, Francesco Serra Cassano

Publication date: 28 March 2006

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02922114

zbMATH Keywords

graphshypersurfacesarea formulaCarnot-Carathéodory metric

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Length, area, volume, other geometric measure theory (28A75) Nilpotent and solvable Lie groups (22E25) Analysis on other specific Lie groups (43A80)

Related Items (52)

The regularity of Euclidean Lipschitz boundaries with prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds ⋮ Strong maximum principle for mean curvature operators on subRiemannian manifolds ⋮ Intrinsic regular submanifolds in Heisenberg groups are differentiable graphs ⋮ Area of intrinsic graphs and coarea formula in Carnot groups ⋮ Convex hull property and exclosure theorems for \(H\)-minimal hypersurfaces in Carnot groups ⋮ Some remarks about parametrizations of intrinsic regular surfaces in the Heisenberg group ⋮ Area-minimizing ruled graphs and the Bernstein problem in the Heisenberg group ⋮ Sub-Riemannian calculus on hypersurfaces in Carnot groups ⋮ Characteristic points, rectifiability and perimeter measure on stratified groups ⋮ The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations ⋮ Regular submanifolds, graphs and area formula in Heisenberg groups ⋮ 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 ⋮ Intrinsic Lipschitz graphs in Heisenberg groups and continuous solutions of a balance equation ⋮ Distributional solutions of Burgers' type equations for intrinsic graphs in Carnot groups of step 2 ⋮ A primer on Carnot groups: homogenous groups, Carnot-Carathéodory spaces, and regularity of their isometries ⋮ On the inner cone property for convex sets in two-step Carnot groups, with applications to monotone sets ⋮ Area formula for regular submanifolds of low codimension in Heisenberg groups ⋮ A proof by calibration of an isoperimetric inequality in the Heisenberg group \({\mathbb{H}}^{n}\) ⋮ Intersections of intrinsic submanifolds in the Heisenberg group ⋮ Pauls rectifiable and purely Pauls unrectifiable smooth hypersurfaces ⋮ First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-Hermitian manifolds ⋮ Intrinsic Lipschitz graphs in Carnot groups of step 2 ⋮ Some remarks on contact variations in the first Heisenberg group ⋮ Intrinsic Difference Quotients ⋮ Unnamed Item ⋮ Smooth approximation for intrinsic Lipschitz functions in the Heisenberg group ⋮ Generalized Jacobi identities and ball-box theorem for horizontally regular vector fields ⋮ Intrinsic differentiability and intrinsic regular surfaces in Carnot groups ⋮ Sets with finite \(\mathbb{H}\)-perimeter and controlled normal ⋮ On the Hausdorff volume in sub-Riemannian geometry ⋮ Differentiability and approximate differentiability for intrinsic Lipschitz functions in Carnot groups and a Rademacher theorem ⋮ Regularity of Lipschitz boundaries with prescribed sub-Finsler mean curvature in the Heisenberg group \(\mathbb{H}^1\) ⋮ Minimal surfaces and harmonic functions in the Heisenberg group ⋮ Regularity estimates for continuous solutions of \(\alpha\)-convex balance laws ⋮ Sub-Riemannian vs. Euclidean dimension comparison and fractal geometry on Carnot groups ⋮ Distributional solutions of Burgers' equation and intrinsic regular graphs in Heisenberg groups ⋮ Sub-Riemannian calculus and monotonicity of the perimeter for graphical strips ⋮ Regularity of minimal intrinsic graphs in 3-dimensional sub-Riemannian structures of step 2 ⋮ Uniqueness of generalized \(p\)-area minimizers and integrability of a horizontal normal in the Heisenberg group ⋮ Poincaré-type inequality for Lipschitz continuous vector fields ⋮ Intrinsic regular surfaces of low codimension in Heisenberg groups ⋮ Intrinsically Lipschitz functions with normal target in Carnot groups ⋮ A gauge field model of modal completion ⋮ Examples of area-minimizing surfaces in the sub-Riemannian Heisenberg group \({\mathbb{H}^1}\) with low regularity ⋮ Uniqueness of Viscosity Mean Curvature Flow Solution in Two Sub-Riemannian Structures ⋮ The Bernstein problem for Lipschitz intrinsic graphs in the Heisenberg group ⋮ Boundedness of singular integrals on \(C^{1,{\alpha}}\) intrinsic graphs in the Heisenberg group ⋮ Schauder estimates at the boundary for sub-Laplacians in Carnot groups ⋮ Unnamed Item ⋮ Stable \(H\)-minimal hypersurfaces ⋮ Lipschitz graphs and currents in Heisenberg groups

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