Remarks on harmonic maps into a cone from a stochastically complete manifold

DOI10.3792/PJAA.75.105zbMath0960.58019OpenAlexW2082298809MaRDI QIDQ1969177

Atsushi Atsuji

Publication date: 7 May 2001

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.75.105

zbMATH Keywords

harmonic mapsminimal submanifoldsstochastically complete Riemannian manifold

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) Harmonic maps, etc. (58E20)

Related Items (4)

Maps from Riemannian manifolds into non-degenerate Euclidean cones ⋮ Compact minimal submanifolds in a large class of Riemannian manifolds ⋮ A second main theorem of Nevanlinna theory for meromorphic functions on complex submanifolds in \(\mathbb C^{n}\) ⋮ The halfspace theorem for minimal hypersurfaces in regions bounded by minimal cones

Cites Work

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• The strong halfspace theorem for minimal surfaces
• A complete minimal surface in \(R^ 3\) between two parallel planes
• Stochastic calculus in manifolds. With an appendix by P.A. Meyer
• Isometric immersions of Riemannian manifolds
• A Complete Bounded Complex Submanifold of C 3
• Probability, Convexity, and Harmonic Maps with Small Image I: Uniqueness and Fine Existence
• On the existence of complete bounded minimal surfaces in ℝn
• A volume estimate for strong subharmonicity and maximum principle on complete Riemannian manifolds

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