Conformally invariant powers of the Laplacian — A complete nonexistence theorem
نویسندگان
چکیده
منابع مشابه
On Conformally Covariant Powers of the Laplacian
We propose and discuss recursive formulae for conformally covariant powers P2N of the Laplacian (GJMS-operators). For locally conformally flat metrics, these describe the non-constant part of any GJMS-operator as the sum of a certain linear combination of compositions of lower order GJMS-operators (primary part) and a second-order operator which is defined by the Schouten tensor (secondary part...
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Recent work in even-dimensional conformal geometry [1],[3], [4], [6] has revealed the importance of conformally invariant powers of the Laplacian on a conformal manifold; that is, of operators Pk whose principal part is the same as ∆ k with respect to a representative of the conformal structure. These invariant powers of the Laplacian were first defined in [5] in terms of the Fefferman-Graham [...
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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...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2004
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-04-00450-3