Sets with finite \(\mathbb{H}\)-perimeter and controlled normal

DOI10.1007/s00209-010-0801-7zbMath1257.49047OpenAlexW2469769548MaRDI QIDQ663231

Davide Vittone, Roberto Monti

Publication date: 14 February 2012

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-010-0801-7

zbMATH Keywords

Heisenberg groupcontinuous normalfinite perimeter sets

Mathematics Subject Classification ID

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Length, area, volume, other geometric measure theory (28A75) Sub-Riemannian geometry (53C17) Set functions and measures on spaces with additional structure (28C99)

Related Items (16)

Eulerian, Lagrangian and Broad continuous solutions to a balance law with non-convex flux. I. ⋮ Multiexponential maps in Carnot groups with applications to convexity and differentiability ⋮ Intrinsic rectifiability via flat cones in the Heisenberg group ⋮ Distributional solutions of Burgers' type equations for intrinsic graphs in Carnot groups of step 2 ⋮ Area-minimizing properties of Pansu spheres in the sub-Riemannian 3-sphere ⋮ A proof by calibration of an isoperimetric inequality in the Heisenberg group \({\mathbb{H}}^{n}\) ⋮ Intrinsic Lipschitz graphs in Carnot groups of step 2 ⋮ Smooth approximation for intrinsic Lipschitz functions in the Heisenberg group ⋮ Minimal surfaces and harmonic functions in the Heisenberg group ⋮ Regularity estimates for continuous solutions of \(\alpha\)-convex balance laws ⋮ Lipschitz approximation of \(\mathbb H\)-perimeter minimizing boundaries ⋮ Distributional solutions of Burgers' equation and intrinsic regular graphs in Heisenberg groups ⋮ Regularity properties of \(H\)-convex sets ⋮ The Gauss-Green theorem in stratified groups ⋮ Poincaré-type inequality for Lipschitz continuous vector fields ⋮ Lipschitz graphs and currents in Heisenberg groups

Cites Work

• Unnamed Item
• Unnamed Item
• Differentiability of intrinsic Lipschitz functions within Heisenberg groups
• Regularity properties of \(H\)-convex sets
• Intrinsic regular hypersurfaces in Heisenberg groups
• Intrinsic regular submanifolds in Heisenberg groups are differentiable graphs
• Distributional solutions of Burgers' equation and intrinsic regular graphs in Heisenberg groups
• A proof by calibration of an isoperimetric inequality in the Heisenberg group \({\mathbb{H}}^{n}\)
• Intrinsic regular graphs in Heisenberg groups vs. weak solutions of non-linear first-order PDEs
• [https://portal.mardi4nfdi.de/wiki/Publication:5689214 Isoperimetric and Sobolev inequalities for Carnot-Carath�odory spaces and the existence of minimal surfaces]
• Rectifiability and perimeter in the Heisenberg group

This page was built for publication: Sets with finite \(\mathbb{H}\)-perimeter and controlled normal