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Maximizing one Laplace eigenvalue on n-dimensional manifolds

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arxiv 2211.15636 v1 pith:3J7VIYTD submitted 2022-11-28 math.AP math.DGmath.FA

Romain Petrides This is my paper · ORCID
classification math.APmath.DGmath.FA
keywords eigenvaluelaplaceclassconformaldimensionexistencelyingmanifold
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abstract

We prove existence and regularity results for the problem of maximization of one Laplace eigenvalue with respect to metrics of same volume lying in a conformal class of a Riemannian manifold of dimension $n\geq 3$.

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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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