Sequences of metrics on compact Riemann surfaces

DOI10.1215/S0012-7094-93-07227-4zbMath0798.11018MaRDI QIDQ1320642

John A. Rhodes

Publication date: 1 November 1994

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Laplace operatorspectral theorycompact Riemann surfacesautomorphic formholomorphic differentialBergmann metrics

Mathematics Subject Classification ID

Conformal metrics (hyperbolic, Poincaré, distance functions) (30F45) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35) Differentials on Riemann surfaces (30F30)

Related Items (9)

Holomorphic line bundles over a tower of coverings ⋮ Limit of Bergman kernels on a tower of coverings of compact Kähler manifolds ⋮ A tower of coverings of quasi-projective varieties ⋮ Asymptotic linearity of the mapping class group and a homological version of the Nielsen-Thurston classification ⋮ Canonical measures on metric graphs and a Kazhdan's theorem ⋮ A tower of Riemann surfaces whose Bergman kernels jump at the roof ⋮ Elliptic operators and covers of Riemannian manifolds ⋮ Limits of canonical forms on towers of Riemann surfaces ⋮ Effective very ampleness of the canonical line bundles on ball quotients

Cites Work

• The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
• The Selberg trace formula for \(\mathrm{PSL}(2,\mathbb R)\). Vol. I
• Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. I, II. (The eigenvalue problem of automorphic forms in the hyperbolic plane. I. II)
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