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Explicit formulas for GJMS-operators and Q-curvatures
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2013 (English)In: Geometric and Functional Analysis, ISSN 1016-443X, E-ISSN 1420-8970, Vol. 23, no 4, 1278-1370 p.Article in journal (Other academic) Published
Abstract [en]

We describe GJMS-operators as linear combinations of compositions of natural second-order differential operators. These are defined in terms of Poincar,-Einstein metrics and renormalized volume coefficients. As special cases, we derive explicit formulas forconformally covariant third and fourth powers of the Laplacian. Moreover, we prove relatedformulas 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. Birkhauser Verlag, Basel, 2009).

Place, publisher, year, edition, pages
2013. Vol. 23, no 4, 1278-1370 p.
Keyword [en]
Conformal Geometry, Laplacian, Q-curvature
National Category
Research subject
URN: urn:nbn:se:uu:diva-160685DOI: 10.1007/s00039-013-0232-9ISI: 000321867400006OAI: oai:DiVA.org:uu-160685DiVA: diva2:452406
Available from: 2011-10-29 Created: 2011-10-29 Last updated: 2013-08-31Bibliographically approved

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Publisher's full texthttp://arxiv.org/abs/1108.0273

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