A probabilistic approach to the Yang-Mills heat equation.

DOI10.1016/S0021-7824(02)01254-0zbMath1042.58021MaRDI QIDQ1408913

Anton Thalmaier, Marc Arnaudon, Robert Otto Bauer

Publication date: 25 September 2003

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

zbMATH Keywords

heat equationBrownian motionparallel transportYang-Mills connectionlocal martingaleYang-Mills energy

Mathematics Subject Classification ID

Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Diffusion processes and stochastic analysis on manifolds (58J65) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (14)

Stochastic Lévy differential operators and Yang–Mills equations ⋮ Yang-Mills fields and random holonomy along Brownian bridges ⋮ Lévy Laplacians, holonomy group and instantons on 4-manifolds ⋮ The Yang-Mills heat semigroup on three-manifolds with boundary ⋮ A stochastic approach to a priori estimates and Liouville theorems for harmonic maps ⋮ Applications of Lévy differential operators in the theory of gauge fields ⋮ Lévy Laplacians and instantons on manifolds ⋮ The Li-Yau-Hamilton estimate and the Yang-Mills heat equation on manifolds with boundary ⋮ Brownian motion with respect to time-changing Riemannian metrics, applications to Ricci flow ⋮ Gradient estimates for the heat equation under the Ricci flow ⋮ Lévy Laplacian on manifold and Yang-Mills heat flow ⋮ Lévy Laplacians in Hida calculus and Malliavin calculus ⋮ Lévy differential operators and Gauge invariant equations for Dirac and Higgs fields ⋮ The Yang-Mills heat equation with finite action in three dimensions

Cites Work

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