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Conformal Invariants from Nodal Sets. I. Negative Eigenvalues and Curvature Prescription

Canzani, Yaiza; Gover, Rod; Jakobson, Dmitry; Ponge, Raphael

Description

In this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators; more specifically, the Graham, Jenne, Mason, and Sparling (GJMS) operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant's Nodal Domain Theorem. We also show that on any manifold of dimension n≥3, there exist many metrics for which our...[Show more]

dc.contributor.authorCanzani, Yaiza
dc.contributor.authorGover, Rod
dc.contributor.authorJakobson, Dmitry
dc.contributor.authorPonge, Raphael
dc.date.accessioned2015-12-07T22:46:04Z
dc.identifier.issn1073-7928
dc.identifier.urihttp://hdl.handle.net/1885/25617
dc.description.abstractIn this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators; more specifically, the Graham, Jenne, Mason, and Sparling (GJMS) operators, which include the Yamabe and Paneitz operators. We give several applications to curvature prescription problems. We establish a version in conformal geometry of Courant's Nodal Domain Theorem. We also show that on any manifold of dimension n≥3, there exist many metrics for which our invariants are nontrivial. We prove that the Yamabe operator can have an arbitrarily large number of negative eigenvalues on any manifold of dimension n≥3. We obtain similar results for some higher order GJMS operators on some Einstein and Heisenberg manifolds. We describe the invariants arising from the Yamabe and Paneitz operators associated to left-invariant metrics on Heisenberg manifolds. Finally, in Appendix, the second named author and Andrea Malchiodi study the Q-curvature prescription problems for noncritical Q-curvatures.
dc.publisherDuke University Press
dc.sourceInternational Mathematics Research Notices
dc.titleConformal Invariants from Nodal Sets. I. Negative Eigenvalues and Curvature Prescription
dc.typeJournal article
local.description.notesImported from ARIES
dc.date.issued2013
local.identifier.absfor010108 - Operator Algebras and Functional Analysis
local.identifier.ariespublicationu4743872xPUB39
local.type.statusPublished Version
local.contributor.affiliationCanzani, Yaiza, McGill University
local.contributor.affiliationGover, Rod, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationJakobson, Dmitry, McGill University
local.contributor.affiliationPonge, Raphael, Seoul National University
local.description.embargo2037-12-31
local.bibliographicCitation.startpage1
local.bibliographicCitation.lastpage45
local.identifier.doi10.1093/imrn/rns295
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
dc.date.updated2015-12-07T11:37:24Z
local.identifier.scopusID2-s2.0-84900020449
local.identifier.thomsonID000335920300004
CollectionsANU Research Publications

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