Osaka Journal of Mathematics

Subelliptic harmonic morphisms

Sorin Dragomir and Ermanno Lanconelli

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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.

Article information

Osaka J. Math., Volume 46, Number 2 (2009), 411-440.

First available in Project Euclid: 19 June 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32V20: Analysis on CR manifolds 53C43: Differential geometric aspects of harmonic maps [See also 58E20]
Secondary: 35H20: Subelliptic equations 58E20: Harmonic maps [See also 53C43], etc.


Dragomir, Sorin; Lanconelli, Ermanno. Subelliptic harmonic morphisms. Osaka J. Math. 46 (2009), no. 2, 411--440.

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