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June 2009 Subelliptic harmonic morphisms
Sorin Dragomir, Ermanno Lanconelli
Osaka J. Math. 46(2): 411-440 (June 2009).

Abstract

We study subelliptic harmonic morphisms i.e. smooth maps $\phi\colon \Omega \to \tilde{\Omega}$ among domains $\Omega \subset \mathbb{R}^{N}$ and $\tilde{\Omega} \subset \mathbb{R}^{M}$, endowed with Hörmander systems of vector fields $X$ and $Y$, that pull back local solutions to $H_{Y} v = 0$ into local solutions to $H_{X} u = 0$, where $H_{X}$ and $H_{Y}$ are Hörmander operators. We show that any subelliptic harmonic morphism is an open mapping. Using a subelliptic version of the Fuglede-Ishihara theorem (due to E. Barletta, [5]) we show that given a strictly pseudoconvex CR manifold $M$ and a Riemannian manifold $N$ for any heat equation morphism $\Psi\colon M \times (0, \infty) \to N \times (0, \infty)$ of the form $\Psi (x,t) = (\phi (x), h(t))$ the map $\phi\colon M \to N$ is a subelliptic harmonic morphism.

Citation

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Sorin Dragomir. Ermanno Lanconelli. "Subelliptic harmonic morphisms." Osaka J. Math. 46 (2) 411 - 440, June 2009.

Information

Published: June 2009
First available in Project Euclid: 19 June 2009

zbMATH: 1175.58005
MathSciNet: MR2549594

Subjects:
Primary: 32V20, 53C43
Secondary: 35H20, 58E20

Rights: Copyright © 2009 Osaka University and Osaka City University, Departments of Mathematics

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Vol.46 • No. 2 • June 2009
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