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April 2000 Smoothness of harmonic maps for hypoelliptic diffusions
Jean Picard
Ann. Probab. 28(2): 643-666 (April 2000). DOI: 10.1214/aop/1019160255

Abstract

Harmonic maps are viewed as maps sending a fixed diffusion to manifold-valued martingales.Under a convexity condition, we prove that the continuity of real-valued harmonic functions implies the continuity of harmonic maps. Then we prove with a probabilistic method that continuous harmonic maps are smooth under Hörmander’s condition; the proof relies on the study of martingales with values in the tangent bundle.

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Jean Picard. "Smoothness of harmonic maps for hypoelliptic diffusions." Ann. Probab. 28 (2) 643 - 666, April 2000. https://doi.org/10.1214/aop/1019160255

Information

Published: April 2000
First available in Project Euclid: 18 April 2002

zbMATH: 1044.58045
MathSciNet: MR1782269
Digital Object Identifier: 10.1214/aop/1019160255

Subjects:
Primary: 58E20, 58G32, 60G48, 60H07

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 2 • April 2000
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