Extremal spectral properties of Otsuki tori

DOI10.1002/mana.201200003zbMath1271.58007arXiv1108.5160OpenAlexW3122144596MaRDI QIDQ4916115

Alexei V. Penskoi

Publication date: 19 April 2013

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.5160

zbMATH Keywords

eigenvaluesLaplacianextremal metricOtsuki tori

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Critical metrics (58E11) Variational methods for eigenvalues of operators (49R05) Manifolds of metrics (especially Riemannian) (58D17)

Related Items

Index of minimal surfaces in the 3-sphere, Bipolar Lawson tau-surfaces and generalized Lawson tau-surfaces, Maximization of Laplace−Beltrami eigenvalues on closed Riemannian surfaces, On Otsuki tori and their Willmore energy, Spectral properties of bipolar surfaces to Otsuki tori, On branched minimal immersions of surfaces by first eigenfunctions, 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, Generalized Lawson tori and Klein bottles

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Upper bounds for eigenvalues of conformal metrics
• A unique extremal metric for the least eigenvalue of the Laplacian on the Klein bottle
• 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
• Isoperimetric inequality for the second eigenvalue of a sphere.
• Spectral properties of bipolar minimal surfaces in \(\mathbb S^4\)
• Laplacian eigenvalue functionals and metric deformations on compact manifolds
• Minimal immersions of Riemannian manifolds
• Minimal submanifolds of low cohomogeneity
• Extremal Metric for the First Eigenvalue on a Klein Bottle
• Minimal Hypersurfaces in a Riemannian Manifold of Constant Curvature