A martingale approach to minimal surfaces

DOI10.1016/j.jfa.2008.06.033zbMath1171.53011arXiv0805.0556OpenAlexW2070904441WikidataQ56211607 ScholiaQ56211607MaRDI QIDQ1017685

Robert W. Neel

Publication date: 12 May 2009

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0805.0556

zbMATH Keywords

minimal surfaceBrownian motionLiouville theoremcouplingmaximum principle at infinityhalfspace theorem

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Diffusion processes and stochastic analysis on manifolds (58J65)

Related Items (2)

The Markov chain Monte Carlo revolution ⋮ The classical theory of minimal surfaces

Cites Work

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• The strong halfspace theorem for minimal surfaces
• Convex hulls of complete minimal surfaces
• Gittins indices in the dynamic allocation problem for diffusion processes
• Liouville-type properties for embedded minimal surfaces
• Maximum principles at infinity
• The \(L^ p\)-integrability of Green's functions and fundamental solutions for elliptic and parabolic equations
• A complete minimal surface in \(R^ 3\) between two parallel planes
• Half-space theorems for minimal surfaces with bounded curvature.
• The topological, geometry and conformal structure of properly embedded minimal surfaces
• Multidimensional diffusion processes.
• Intersection of minimal surfaces of bounded curvature
• Hadamard's and Calabi-Yau's conjectures on negatively curved and minimal surfaces

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