Smoothness of harmonic maps for hypoelliptic diffusions

被引：6

作者：

Picard, J ^{[1
]}

机构：

[1] Univ Blaise Pascal, CNRS UMR 6620, Lab Math Appl, F-63177 Clermont Ferrand, France

来源：

ANNALS OF PROBABILITY | 2000年 / 28卷 / 02期

关键词：

harmonic maps; manifold-valued martingales; stochastic calculus on; manifolds; Malliavin calculus;

D O I：

10.1214/aop/1019160255

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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 Hormander's condition; the proof relies on the study of martingales with values in the tangent bundle.

引用

页码：643 / 666

页数：24

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