Explicit Formulas for GJMS-Operators and Q-Curvatures

We describe GJMS-operators as linear combinations of compositions of natural second-order differential operators. These are defined in terms of Poincaré–Einstein metrics and renormalized volume coefficients. As special cases, we derive explicit formulas for conformally covariant third and fourth pow...

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Bibliographic Details
Published inGeometric and functional analysis Vol. 23; no. 4; pp. 1278 - 1370
Main Author Juhl, Andreas
Format Journal Article
LanguageEnglish
Published Basel Springer Basel 01.08.2013
Subjects
Analysis
Conformal Geometry
Laplacian
Matematik
Mathematics
Mathematics and Statistics
Q-curvature
53A55
53B20
35J30
53A30
Secondary 35Q76
58J50
Primary 05A19
53C25
Online AccessGet full text
ISSN1016-443X
1420-8970
1420-8970
DOI10.1007/s00039-013-0232-9

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Summary:We describe GJMS-operators as linear combinations of compositions of natural second-order differential operators. These are defined in terms of Poincaré–Einstein metrics and renormalized volume coefficients. As special cases, we derive explicit formulas for conformally covariant third and fourth powers of the Laplacian. Moreover, we prove related formulas for all Branson’s Q -curvatures. The results settle and refine conjectural statements in earlier works. The proofs rest on the theory of residue families introduced in Juhl (Progress in Mathematics, vol. 275. Birkhäuser Verlag, Basel, 2009 ).
ISSN:1016-443X
1420-8970
1420-8970
DOI:10.1007/s00039-013-0232-9