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Maximization of higher order eigenvalues and applications

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arxiv 1504.07465 v1 pith:T766CGEQ submitted 2015-04-28 math.DG

N. Nadirashvili , Y. Sire This is my paper · ORCID
classification math.DG
keywords citeeigenvalueshighermaximizationorderappearapplicationsboundaryless
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The present paper is a follow up of our paper \cite{nS}. We investigate here the maximization of higher order eigenvalues in a conformal class on a smooth compact boundaryless Riemannian surface. Contrary to the case of the first nontrivial eigenvalue as shown in \cite{nS}, bubbling phenomena appear.

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  1. Extremising eigenvalues of the GJMS operators in a fixed conformal class

    math.DG 2025-05 conditional novelty 8.0 of 10

    Conformal eigenvalue extremals for GJMS operators of any order s and any index k exist under a gap condition for positive eigenvalues and unconditionally for negative eigenvalues, assuming a unique continuation property.

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