Linearized pseudo-Einstein equations on the Heisenberg group

Elisabetta Barletta, Sorin Dragomir, Howard Jacobowitz

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We study the pseudo-Einstein equation R11¯=0 on the Heisenberg group H1=C×R. We consider first order perturbations θϵ0+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 (H10) 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|→+∞.

Original languageEnglish (US)
Pages (from-to)95-105
Number of pages11
JournalJournal of Geometry and Physics
StatePublished - Feb 1 2017

All Science Journal Classification (ASJC) codes

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


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