Maximization of the second conformal eigenvalue of spheres

DOI10.1090/S0002-9939-2014-12095-8zbMath1293.35185arXiv1206.0229MaRDI QIDQ5418549

Romain Petrides

Publication date: 4 June 2014

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

Full work available at URL: https://arxiv.org/abs/1206.0229

zbMATH Keywords

Laplace-Beltrami operatorround sphereconformal eigenvalues

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items (15)

Two balls maximize the third Neumann eigenvalue in hyperbolic space ⋮ Existence and classification of \(\mathbb{S}^1\)-invariant free boundary minimal annuli and Möbius bands in \(\mathbb{B}^n\) ⋮ Maximization of the second Laplacian eigenvalue on the sphere ⋮ Extremal metrics for combinations of Laplace eigenvalues and minimal surfaces into ellipsoids ⋮ Maximizers beyond the hemisphere for the second Neumann eigenvalue ⋮ Maximization of Laplace−Beltrami eigenvalues on closed Riemannian surfaces ⋮ Some results on higher eigenvalue optimization ⋮ The spectrum of the Laplacian: A geometric approach ⋮ Index of minimal spheres and isoperimetric eigenvalue inequalities ⋮ Continuity of eigenvalues and shape optimisation for Laplace and Steklov problems ⋮ Isoperimetric inequalities for higher eigenvalues of the Laplace-Beltrami operator on surfaces ⋮ An isoperimetric inequality for the second non-zero eigenvalue of the Laplacian on the projective plane ⋮ An isoperimetric inequality for Laplace eigenvalues on the sphere ⋮ Extremal metrics for the Paneitz operator on closed four-manifolds ⋮ Robin spectrum: two disks maximize the third eigenvalue

Cites Work

• Upper bounds for eigenvalues of conformal metrics
• Immersions minimales, première valeur propre du laplacien et volume conforme. (Minimal immersions, first eigenvalue of the Laplacian and conformal volume)
• Extremal eigenvalues of the Laplacian in a conformal class of metrics: the `conformal spectrum'
• Isoperimetric inequality for the second eigenvalue of a sphere.
• Maximization of the second positive Neumann eigenvalue for planar domains
• Riemannian Metrics with Large λ 1
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