We study subelliptic harmonic morphisms i.e. smooth maps $\phi: \Omega \to \tilde\Omega$ 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 $\Psi: M \times (0, \infty) \to N \times (0, \infty)$ of the form $\Psi(x,t) = ( \phi (x), h(t))$ the map $\phi : M \to N$ is a subelliptic harmonic morphism.

Subelliptic harmonic morphisms

DRAGOMIR, Sorin;
2009-01-01

Abstract

We study subelliptic harmonic morphisms i.e. smooth maps $\phi: \Omega \to \tilde\Omega$ 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 $\Psi: M \times (0, \infty) \to N \times (0, \infty)$ of the form $\Psi(x,t) = ( \phi (x), h(t))$ the map $\phi : M \to N$ is a subelliptic harmonic morphism.
2009
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11563/683
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