On the rigidity of certain discrete groups and algebraic varieties

DOI10.1007/BF01458080zbMath0624.32019OpenAlexW1988747202MaRDI QIDQ1092206

Juergen Jost, Shing Tung Yau

Publication date: 1987

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

Full work available at URL: https://eudml.org/doc/164301

zbMATH Keywords

compactificationTeichmüller spacerigiditymodular groupharmonic mapsmoduli space of Riemann surfacesdiscrete automorphism groupbiholomorphically equivalenthomotopically equivalentKähler varietylocally symmetric complex spaces

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) (32M15) Complex Lie groups, group actions on complex spaces (32M05) Compactification of analytic spaces (32J05) Automorphic functions in symmetric domains (32N15)

Related Items (9)

Modular Symbols and the Topological Nonrigidity of Arithmetic Manifolds ⋮ On the Singular Set of Harmonic Maps into DM-Complexes ⋮ Strong rigidity of irreducible quotients of polydiscs of finite volume ⋮ $C^1$ estimates for the Weil-Petersson metric ⋮ Essential regularity of the model space for the Weil-Petersson metric ⋮ Foliated Plateau problem. II: Harmonic maps of foliations ⋮ A boundary value problem for Hermitian harmonic maps and applications ⋮ The heat equation and harmonic maps of complete manifolds ⋮ A nonlinear elliptic system for maps from Hermitian to Riemannian manifolds and rigidity theorems in Hermitian geometry

Cites Work

• Unnamed Item
• Unnamed Item
• Harmonic maps between surfaces (with a special chapter on conformal mappings)
• The complex-analyticity of harmonic maps and the strong rigidity of compact Kaehler manifolds
• Nonpositively curved manifolds of higher rank
• Chern forms and the Riemann tensor for the moduli space of curves
• Harmonic maps of the moduli space of compact Riemann surfaces
• On a natural algebraic affine connection on the space of almost complex structures and the curvature of Teichmüller space with respect to its Weil-Petersson metric
• The Ahlfors-Schwarz lemma in several complex variables
• Complex-analyticity of harmonic maps, vanishing and Lefschetz theorems
• Analytic cycles and vector bundles on non-compact algebraic varieties
• Harmonic maps and the topology of stable hypersurfaces and manifolds with non-negative Ricci curvature
• Geodesic length functions and the Nielsen problem
• Compactification of arithmetic quotients of bounded symmetric domains
• On the moduli Jacobian varieties
• Some metric properties of arithmetic quotients o f symmetric spaces and an extension theorem
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• Discrete groups of motions of manifolds of nonpositive curvature

This page was built for publication: On the rigidity of certain discrete groups and algebraic varieties