A stochastic approach to a priori estimates and Liouville theorems for harmonic maps

DOI10.1016/j.bulsci.2011.07.014zbMath1242.58020OpenAlexW2058325905WikidataQ125120593 ScholiaQ125120593MaRDI QIDQ645952

Anton Thalmaier, Feng-Yu Wang

Publication date: 11 November 2011

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2011.07.014

zbMATH Keywords

gradient estimateBrownian motionRiemannian manifoldRicci curvatureLiouville theoremharmonic mapprobabilistic methodBismut formulanonlinear martingalestochastic development

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes and stochastic analysis on manifolds (58J65) Harmonic maps, etc. (58E20) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (8)

Quantitative \(C^{1}\)-estimates by Bismut formulae ⋮ Scattering theory without injectivity radius assumptions, and spectral stability for the Ricci flow ⋮ A stochastic approach to the harmonic map heat flow on manifolds with time-dependent Riemannian metric ⋮ Martingales on manifolds with time-dependent connection ⋮ Bismut-Stroock Hessian formulas and local Hessian estimates for heat semigroups and harmonic functions on Riemannian manifolds ⋮ A study of backward stochastic differential equation on a Riemannian manifold ⋮ Heat flow regularity, Bismut-Elworthy-Li's derivative formula, and pathwise couplings on Riemannian manifolds with Kato bounded Ricci curvature ⋮ Scattering theory for the Hodge Laplacian

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