Martingales arising from minimal submanifolds and other geometric contexts

zbMath1322.58023arXiv1210.4033MaRDI QIDQ491444

Robert W. Neel

Publication date: 25 August 2015

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.4033

zbMATH Keywords

Brownian motionmartingalesminimal submanifoldCartan-Hadamard manifolds

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes and stochastic analysis on manifolds (58J65) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (1)

Geometric and Martin boundaries of a Cartan-Hadamard surface

Cites Work

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• On parabolicity and area growth of minimal surfaces
• Convergence of martingales on a Riemannian manifold
• The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups
• Brownian motion, geometry, and generalizations of Picard's little theorem
• Brownian motion and harmonic functions on rotationally symmetric manifolds
• Exit probability estimates for martingales in geodesic balls, using curvature
• Differentiable and analytic families of continuous martingales in manifolds with connection
• Eigenvalue estimates for submanifolds with locally bounded mean curvature
• Transience and capacity of minimal submanifolds
• A stochastic representation for mean curvature type geometric flows
• Brownian motion and Dirichlet problems at infinity
• The radial part of a \(\Gamma\)-martingale and a non-implosion theorem
• Martingales on noncompact manifolds: Maximal inequalities and prescribed limits
• Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds

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