## Abstract

We study the pseudo-Einstein equation R_{11¯}=0 on the Heisenberg group H_{1}=C×R. We consider first order perturbations θ_{ϵ}=θ_{0}+ϵθ and linearize the pseudo-Einstein equation about θ_{0} (the canonical Tanaka–Webster flat contact form on H_{1} thought of as a strictly pseudoconvex CR manifold). If θ=e^{2u}θ_{0} the linearized pseudo-Einstein equation is Δ_{b}u−4|Lu|^{2}=0 where Δ_{b} is the sublaplacian of (H_{1},θ_{0}) and L¯ is the Lewy operator. We solve the linearized pseudo-Einstein equation on a bounded domain Ω⊂H_{1} by applying subelliptic theory i.e. existence and regularity results for weak subelliptic harmonic maps. We determine a solution u to the linearized pseudo-Einstein equation, possessing Heisenberg spherical symmetry, and such that u(x)→−∞ as |x|→+∞.

Original language | English (US) |
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Pages (from-to) | 95-105 |

Number of pages | 11 |

Journal | Journal of Geometry and Physics |

Volume | 112 |

DOIs | |

State | Published - Feb 1 2017 |

## All Science Journal Classification (ASJC) codes

- Mathematical Physics
- Physics and Astronomy(all)
- Geometry and Topology