Extremal metrics for the first eigenvalue of the Laplacian in a conformal class

DOI10.1090/S0002-9939-02-06948-4zbMath1027.58010OpenAlexW1632724111MaRDI QIDQ4791508

Said Ilias, Ahmad El Soufi

Publication date: 28 January 2003

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-02-06948-4

zbMATH Keywords

harmonic mapsextremal metricsfirst eigenvalue of the Laplacianconformal classes

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Critical metrics (58E11)

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Cites Work

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• Generic properties of the eigenvalue of the Laplacian for compact Riemannian manifolds
• Immersions minimales, première valeur propre du laplacien et volume conforme. (Minimal immersions, first eigenvalue of the Laplacian and conformal volume)
• Berger's isoperimetric problem and minimal immersions of surfaces
• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
• Riemannian manifolds admitting isometric immersions by their first eigenfunctions
• Morse index of \(p\)-harmonic maps
• A Report on Harmonic Maps
• Riemannian Metrics with Large λ 1
• Convex Analysis

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