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Yaiza Canzani
On the multiplicity of eigenvalues of conformally covariant operators
(Sur la multiplicité des valeurs propres d’opérateurs covariants conformes)
Annales de l'institut Fourier, 64 no. 3 (2014), p. 947-970, doi: 10.5802/aif.2870
Article PDF | Reviews MR 3330160 | Zbl 06387297
Class. Math.: 53A30, 58C40
Keywords: Multiplicity, eigenvalues, conformal geometry, conformally covariant operators, GJMS operators.

Résumé - Abstract

Let $(M,g)$ be a compact Riemannian manifold and $P_g$ an elliptic, formally self-adjoint, conformally covariant operator of order $m$ acting on smooth sections of a bundle over $M$. We prove that if $P_g$ has no rigid eigenspaces (see Definition 2.2), the set of functions $f\in C^\infty (M, \mathbb{R (Met wmuich tP_g{e^fg} has nnli seimpe onon-zeroeigenvalues os ia es idul get on C$^\infty (M, mathbb{R (M. Asa comnseue1ced w prove that if $P_g$ has no rigid eigenspaces (or ande nseset of fetryics the nalilonon-zeroeigenvalues oareseimpe oor andes idul get of fetryicson Che s$^\infty ($top:ology We palsoprove that ihe sigenvalues of$P_g$ hdeped copninguus i sn 2$$ hn Che s$^\infty ($top:ology,proveide $P_g$ as itraongi slliptic,. Asa nappeicition af orr lordk, w phorwthat if $P_g$ hctissn 2$^\infty (M,(Me(e.g.GJMS operators., titsonon-zeroeigenvalues oaresenvercal-i seimpe ./p><

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<&opyr; nnales de lL'Istitut Fourier< - ISSN (éect>ronque1) : 1777-5310