Contact equations, Lipschitz extensions and isoperimetric inequalities

DOI10.1007/s00526-010-0309-3zbMath1195.49053arXiv0711.5003OpenAlexW2027583332MaRDI QIDQ5961992

Valentino Magnani

Publication date: 16 September 2010

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

Full work available at URL: https://arxiv.org/abs/0711.5003

zbMATH Keywords

compact Riemannian manifoldsAllcock groupsfirst-order nonlinear system of PDEsLipschitz extensionslocally Lipschitz mappingsRumin complex

Mathematics Subject Classification ID

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Nilpotent and solvable Lie groups (22E25) Sub-Riemannian geometry (53C17)

Related Items (8)

Global contact and quasiconformal mappings of Carnot groups ⋮ Filling inequalities for nilpotent groups through approximations. ⋮ Undistorted fillings in subsets of metric spaces ⋮ Unextendable Intrinsic Lipschitz Curves: ⋮ The effect of projections on dimension in the Heisenberg group ⋮ Nonexistence of horizontal Sobolev surfaces in the Heisenberg group ⋮ TOWARDS DIFFERENTIAL CALCULUS IN STRATIFIED GROUPS ⋮ Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups

Cites Work

• Lipschitz continuity, Aleksandrov theorem and characterizations for \(H\)-convex functions
• Conformality and \(Q\)-harmonicity in Carnot groups
• Differentiating maps into \(L^1\), and the geometry of BV functions
• Rectifiability and Lipschitz extensions into the Heisenberg group
• Carnot-Carathéodory metrics and quasiisometries of symmetric spaces of rank 1
• Lipschitz continuity, global smooth approximations and extension theorems for Sobolev functions in Carnot-Carathéodory spaces
• Quadratic isometric functions of the Heisenberg groups. A combinatorial proof
• An isoperimetric inequality for the Heisenberg groups
• Equivalence of geometric and combinatorial Dehn functions.
• Lipschitz extensions into jet space Carnot groups
• The homotopy groups of the integral cycle groups
• TOWARDS DIFFERENTIAL CALCULUS IN STRATIFIED GROUPS
• Lipschitz Non-extension Theorems into Jet Space Carnot Groups
• Sobolev met Poincaré
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• Riemannian Geometry
• Lifts of Lipschitz maps and horizontal fractals in the Heisenberg group
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