Weak Fubini property and infinity harmonic functions in Riemannian and sub-Riemannian manifolds

DOI10.1090/S0002-9947-2012-05612-1zbMath1282.53025OpenAlexW2086970480WikidataQ115285563 ScholiaQ115285563MaRDI QIDQ4915114

Juan J. Manfredi, Federica Dragoni, Davide Vittone

Publication date: 16 April 2013

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-2012-05612-1

zbMATH Keywords

Riemannian manifoldsCarnot-Carathéodory spacesabsolutely minimizing Lipschitz extensioninfinity Laplace equation

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Nilpotent and solvable Lie groups (22E25) Sub-Riemannian geometry (53C17) Subelliptic equations (35H20)

Related Items (8)

Random walks and random tug of war in the Heisenberg group ⋮ A Rademacher type theorem for Hamiltonians \(H(x, p)\) and an application to absolute minimizers ⋮ The Aronsson equation for absolute minimizers of supremal functionals in Carnot–Carathéodory spaces ⋮ Existence and uniqueness of \(\infty \)-harmonic functions under assumption of \(\infty \)-Poincaré inequality ⋮ On the \(\infty \)-Laplacian on Carnot groups ⋮ \(L^\infty\)-variational problems associated to measurable Finsler structures ⋮ Intrinsic geometry and analysis of diffusion processes and \(L^{\infty}\)-variational problems ⋮ Starshapedeness for fully non‐linear equations in Carnot groups

Cites Work

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• A tour of the theory of absolutely minimizing functions
• Equivalence of AMLE, strong AMLE, and comparison with cones in metric measure spaces
• Optimal Lipschitz extensions and the infinity Laplacian
• Surface measures in Carnot-Carathéodory spaces

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