Graphs of bounded variation, existence and local boundedness of non-parametric minimal surfaces in Heisenberg groups

DOI10.1515/acv-2013-0105zbMath1304.49084OpenAlexW2335293190MaRDI QIDQ468543

Francesco Serra Cassano, Davide Vittone

Publication date: 7 November 2014

Published in: Advances in Calculus of Variations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/acv-2013-0105

zbMATH Keywords

Heisenberg group bounded variation minimal surfaces sub-Riemannian geometry

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Sub-Riemannian geometry (53C17)

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A measure zero universal differentiability set in the Heisenberg group ⋮ Improved Lipschitz approximation of \(H\)-perimeter minimizing boundaries ⋮ Porosity, differentiability and Pansu's theorem ⋮ The Cheeger problem in abstract measure spaces ⋮ Intrinsic Lipschitz graphs in Carnot groups of step 2 ⋮ Smooth approximation for intrinsic Lipschitz functions in the Heisenberg group ⋮ Rearrangements in metric spaces and in the Heisenberg group ⋮ Uniform Gaussian bounds for subelliptic heat kernels and an application to the total variation flow of graphs over Carnot groups ⋮ Minimal surfaces and harmonic functions in the Heisenberg group ⋮ Regularity of mean curvature flow of graphs on Lie groups free up to step 2 ⋮ Structure of porous sets in Carnot groups ⋮ Lipschitz approximation of \(\mathbb H\)-perimeter minimizing boundaries ⋮ The Gauss-Green theorem in stratified groups ⋮ Uniqueness of generalized \(p\)-area minimizers and integrability of a horizontal normal in the Heisenberg group ⋮ Poincaré-type inequality for Lipschitz continuous vector fields ⋮ A gauge field model of modal completion ⋮ The Bernstein problem for Lipschitz intrinsic graphs in the Heisenberg group ⋮ Lipschitz minimizers for a class of integral functionals under the bounded slope condition

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