Metrics on a closed surface of genus two which maximize the first eigenvalue of the Laplacian

DOI10.1016/j.crma.2018.11.008zbMath1408.58023arXiv1704.06384OpenAlexW2964351250WikidataQ128896423 ScholiaQ128896423MaRDI QIDQ1713495

Toshihiro Shoda, Shin Nayatani

Publication date: 25 January 2019

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.06384

zbMATH Keywords

Bolza surfaceJakobson-Levitin-Nadirashvili-Nigam-Polterovich conjecturemaximize normalized first eigenvalue

Mathematics Subject Classification ID

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

Related Items (17)

Spherical conical metrics and harmonic maps to spheres ⋮ On the first eigenvalue of the Laplacian on compact surfaces of genus three ⋮ On the Friedlander-Nadirashvili invariants of surfaces ⋮ The first eigenvalue of the Laplacian on orientable surfaces ⋮ Extremal metrics for combinations of Laplace eigenvalues and minimal surfaces into ellipsoids ⋮ First eigenvalue of the Laplacian on compact surfaces for large genera ⋮ Some recent developments on the Steklov eigenvalue problem ⋮ Index of minimal spheres and isoperimetric eigenvalue inequalities ⋮ Sharp asymptotics of the first eigenvalue on some degenerating surfaces ⋮ Systolically extremal nonpositively curved surfaces are flat with finitely many singularities ⋮ On branched minimal immersions of surfaces by first eigenfunctions ⋮ On the Yang-Yau inequality for the first Laplace eigenvalue ⋮ Isoperimetric inequalities for higher eigenvalues of the Laplace-Beltrami operator on surfaces ⋮ An isoperimetric inequality for Laplace eigenvalues on the sphere ⋮ Large Steklov eigenvalues via homogenisation on manifolds ⋮ Existence of metrics maximizing the first eigenvalue on non-orientable surfaces ⋮ Robin spectrum: two disks maximize the third eigenvalue

Cites Work

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• Existence and regularity of maximal metrics for the first Laplace eigenvalue on surfaces
• Index and flat ends of minimal surfaces
• Lower bounds for the Morse index of complete minimal surfaces in Euclidean 3-space
• On complete minimal surfaces with finite Morse index in three manifolds
• Berger's isoperimetric problem and minimal immersions of surfaces
• Morse index and Gauss maps of complete minimal surfaces in Euclidean 3- space
• Conformal Spectrum and Harmonic maps
• First eigenvalue of symmetric minimal surfaces in $\mathbb{S}^3$
• Deformations of Symmetric CMC Surfaces in the 3-Sphere

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