TY - JOUR
T1 - Linearized pseudo-Einstein equations on the Heisenberg group
AU - Barletta, Elisabetta
AU - Dragomir, Sorin
AU - Jacobowitz, Howard
N1 - Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2017/2/1
Y1 - 2017/2/1
N2 - 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|→+∞.
AB - 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|→+∞.
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U2 - 10.1016/j.geomphys.2016.10.020
DO - 10.1016/j.geomphys.2016.10.020
M3 - Article
AN - SCOPUS:84998611001
SN - 0393-0440
VL - 112
SP - 95
EP - 105
JO - Journal of Geometry and Physics
JF - Journal of Geometry and Physics
ER -