CR invariant powers of the sub-Laplacian

By C. Graham. 2003

118 citations recorded by the source corpus.

Abstract CR invariant differential operators on densities with leading part a power of the sub-Laplacian are derived. One family of such operators is constructed from the ‘‘conformally invariant powers of the Laplacian’’ via the Fefferman metric; the powers which arise for these operators are bounded in terms of the dimension. A second family is derived from a CR tractor calculus which is developed here; this family includes operators for every positive power of the sub-Laplacian. This result together with work of Čap, Slovák and Souček imply in three dimensions the existence of a curved analogue of each such operator in ﬂat space.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/30d75d942a268d141e96af6a423d01edd5ed8bd9

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

An extension problem for the CR fractional Laplacian (2013, methodology): “Fractional CR covariant operators of order 2γ, γ ∈ R, may be defined from scattering theory on a Kähler-Einstein manifold X [21, 45, 40, 33], they are pseudodifferential operators whose principal symbol agrees with the pure fractional powers of the CR sub–Laplacian (−∆b) on the boundaryM = ∂X .”
Moser-Trudinger and Beckner-Onofri's inequalities on the CR sphere (2007, methodology): “aturality of the operators Ad(W) and A′ Q(W) is expressed by the intertwining relations in (1.38), (1.42). In the case dinteger the operators Ad(W) coincide with those obtained intrinsecally in [FH], [GG], [Hi], within the class of contact forms {Wθ}. 24 2. Adams and Moser-Trudinger inequalitieson t”
Conformally invariant powers of the Laplacian — A complete nonexistence theorem (2004, unknown): “In [11] there is a construction of CR invariant powers of the sub-Laplacian that generates curved analogues for most but not all the invariant operators from the CR (cid:13)at setting.”
Conformally Invariant Powers of the Laplacian, Q-Curvature, and Tractor Calculus (2002, background): “It should also be pointed out that the results and ideas in this paper should have analogues for CR structures, where one would instead be involved with CR-invariant powers of the sub-Laplacian [ 30 ] and the ambient construction of C. Fefferman [24].”