Linearized pseudo-Einstein equations on the Heisenberg group

We study the pseudo-Einstein equation R11¯=0 on the Heisenberg group H1=C×R. We consider first order perturbations θϵ=θ0+ϵθ and linearize the pseudo-Einstein equation about θ0 (the canonical Tanaka–Webster flat contact form on H1 thought of as a strictly pseudoconvex CR manifold). If θ=e2uθ0 the lin...

Full description

Saved in:
Bibliographic Details
Published in:Journal of geometry and physics 2017-02, Vol.112, p.95-105
Main Authors: Barletta, Elisabetta, Dragomir, Sorin, Jacobowitz, Howard
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study the pseudo-Einstein equation R11¯=0 on the Heisenberg group H1=C×R. We consider first order perturbations θϵ=θ0+ϵθ and linearize the pseudo-Einstein equation about θ0 (the canonical Tanaka–Webster flat contact form on H1 thought of as a strictly pseudoconvex CR manifold). If θ=e2uθ0 the linearized pseudo-Einstein equation is Δbu−4|Lu|2=0 where Δb is the sublaplacian of (H1,θ0) and L¯ is the Lewy operator. We solve the linearized pseudo-Einstein equation on a bounded domain Ω⊂H1 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|→+∞.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2016.10.020