CR Invariant powers of the sub-Laplacian

A. Rod Gover; C. Robin Graham

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arXiv · math/0301092

CR Invariant powers of the sub-Laplacian

A. Rod Gover·C. Robin Graham

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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 Cap, Slovak and Soucek imply in three dimensions the existence of a curved analogue of each such operator in flat space.

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A. Rod Gover, C. Robin Graham. 2003-01-09. CR Invariant powers of the sub-Laplacian. https://arxiv.org/abs/math/0301092

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