On the volumes of complex hyperbolic manifolds

DOI10.1215/S0012-7094-96-08422-7zbMath0866.53036MaRDI QIDQ1815368

Frédéric Paulin, Sa'ar Hersonsky

Publication date: 20 July 1997

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

zbMATH Keywords

volumeHeisenberg groupnegative curvaturelocally symmetric spacecomplex hyperbolic geometry

Mathematics Subject Classification ID

Differential geometry of symmetric spaces (53C35) Homogeneous complex manifolds (32M10) Non-Euclidean differential geometry (53A35)

Related Items (13)

Maximal holonomy of infra-nilmanifolds with $2$-dimensional quaternionic Heisenberg geometry ⋮ ON THE VOLUMES OF COMPLEX HYPERBOLIC MANIFOLDS WITH CUSPS ⋮ Lower bound for the volumes of quaternionic hyperbolic orbifolds ⋮ On the volumes of cusped, complex hyperbolic manifolds and orbifolds ⋮ Discreteness of hyperbolic isometries by test maps ⋮ Counting and equidistribution in Heisenberg groups ⋮ Balls in complex hyperbolic manifolds ⋮ A lower bound for the volumes of complex hyperbolic orbifolds ⋮ On volumes of complex hyperbolic orbifolds ⋮ ON DISCRETENESS OF SUBGROUPS OF QUATERNIONIC HYPERBOLIC ISOMETRIES ⋮ Prescribing the behaviour of geodesics in negative curvature ⋮ Effective very ampleness of the canonical line bundles on ball quotients ⋮ New non-arithmetic complex hyperbolic lattices

Cites Work

• Arithmetic subgroups of algebraic groups
• Notes on non-discrete subgroups of Û(1,n;F)
• Volume and bounded cohomology
• The irregularities of Hirzebruch's examples of surfaces of general type with \(c_1^2=3 c_2\)
• Dirichlet polyhedra for dihedral groups acting on complex hyperbolic space
• Hirzebruch's proportionality theorem in the non-compact case
• Möbius transformations in several dimensions
• Covolume estimates for discrete groups of hyperbolic isometries having parabolic elements
• Uniform discreteness and Heisenberg translations
• The first Betti number of the smallest closed hyperbolic 3-manifold
• Harmonic maps into singular spaces and \(p\)-adic superrigidity for lattices in groups of rank one
• Almost convex groups and the eight geometries
• On the volumes of cusped, complex hyperbolic manifolds and orbifolds
• Compact Clifford-Klein forms of symmetric spaces
• Notes on elements of U(1,n;\({\mathbb{C}})\)
• The cusped hyperbolic 3-orbifold of minimum volume
• The Noncompact Hyperbolic 3-Manifold of Minimal Volume
• An Algebraic Surface with K Ample, (K 2 ) = 9, p g = q = 0
• Invariants of Arithmetic Ball Quotient Surfaces
• SHIMIZU’S LEMMA FOR COMPLEX HYPERBOLIC SPACE
• A Generalization of the Shimizu-Leutbecher and Jorgensen Inequalities to Mobius Transformations in R N
• On Ford isometric spheres in complex hyperbolic space
• The Geometries of 3-Manifolds
• FUNDAMENTAL DOMAINS FOR LATTICES IN RANK ONE SEMISIMPLE LIE GROUPS
• Almost flat manifolds
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the volumes of complex hyperbolic manifolds