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Critical metrics of eigenvalue functionals via Clarke subdifferential

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arxiv 2403.07841 v2 pith:5IPUN2VX submitted 2024-03-12 math.DG math.FAmath.SP

Romain Petrides , David Tewodrose This is my paper · ORCID
classification math.DGmath.FAmath.SP
keywords criticalmetricsclarkeconformaleigenvaluesfunctionalslaplacianoperators
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We set up a new framework to study critical points of functionals defined as combinations of eigenvalues of operators with respect to a given set of parameters: Riemannian metrics, potentials, etc. Our setting builds upon Clarke's differentiation theory to provide a novel understanding of critical metrics. In particular, we unify and refine previous research carried out on Laplace and Steklov eigenvalues. We also use our theory to tackle original examples such as the conformal GJMS operators, the conformal Laplacian, and the Laplacian with mixed boundary conditions.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Eigenvalue optimization in higher dimensions and $p$-harmonic maps

    math.SP 2026-01 conditional novelty 8.0 of 10

    In dimensions m≥3, normalized Laplace eigenvalue optimization functionals admit maximizers, and all absolutely continuous maximizers are characterized by p-harmonic maps into spheres.

  2. Maximizing higher eigenvalues in dimensions three and above

    math.SP 2025-06 conditional novelty 8.0 of 10

    For every closed manifold of dimension at least 3 and every k, the maximal k-th eigenvalue functional is attained by a measure induced by a locally stable harmonic map into a sphere.

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