Riemann surfaces with large first eigenvalue

DOI10.1007/BF02790263zbMath0981.30031OpenAlexW2081266914MaRDI QIDQ5941779

Robert Brooks, Eran Makover

Publication date: 21 March 2002

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02790263

zbMATH Keywords

Laplace-Beltrami operatorAhlfors-Schwarz lemmaSelberg conjecture

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Compact Riemann surfaces and uniformization (30F10) Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (14)

The moduli space of Riemann surfaces of large genus ⋮ Small eigenvalues of closed Riemann surfaces for large genus ⋮ Poisson-Dirichlet distribution for random Belyi surfaces ⋮ Near optimal spectral gaps for hyperbolic surfaces ⋮ Some recent developments on the Steklov eigenvalue problem ⋮ The spectrum of the Laplacian: A geometric approach ⋮ Conformal upper bounds for the eigenvalues of the Laplacian and Steklov problem ⋮ Systole and \(\lambda_{2g-2}\) of closed hyperbolic surfaces of genus \(g\) ⋮ Existence and regularity of maximal metrics for the first Laplace eigenvalue on surfaces ⋮ On largeness and multiplicity of the first eigenvalue of finite area hyperbolic surfaces ⋮ Spectre et géométrie conforme des variétés compactes à bord ⋮ Existence and geometric structure of metrics on surfaces which extremize eigenvalues ⋮ Topological properties of eigenfunctions of Riemannian surfaces ⋮ The first eigenvalue of a Riemann surface

Cites Work

• On the bipartition of graphs
• Cubic graphs and the first eigenvalue of a Riemann surface
• Platonic surfaces
• On Selberg's eigenvalue conjecture
• A Generalization of the Ahlfors-Schwarz Lemma
• The first eigenvalue of a Riemann surface
• An Extension of Schwarz's Lemma
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