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Harmonic maps and representations of non-uniform lattices of $PU (m, 1)$

Vincent Koziarz, Julien Maubon (2008)

Annales de l’institut Fourier

We study representations of lattices of $PU (m, 1)$ into $PU (n, 1)$ . We show that if a representation is reductive and if $m$ is at least 2, then there exists a finite energy harmonic equivariant map from complex hyperbolic $m$ -space to complex hyperbolic $n$ -space. This allows us to give a differential geometric proof of rigidity results obtained by M. Burger and A. Iozzi. We also define a new invariant associated to representations into $PU (n, 1)$ of non-uniform lattices in $PU (1, 1)$ , and more generally of fundamental groups of orientable...

Harmonic maps into singular spaces and $p$ -adic superrigidity for lattices in groups of rank one

Michael Gromov, Richard Schoen (1992)

Publications Mathématiques de l'IHÉS

Holomorphic actions, Kummer examples, and Zimmer program

Serge Cantat, Abdelghani Zeghib (2012)

Annales scientifiques de l'École Normale Supérieure

We classify compact Kähler manifolds $M$ of dimension $n \geq 3$ on which acts a lattice of an almost simple real Lie group of rank $\geq n - 1$ . This provides a new line in the so-called Zimmer program, and characterizes certain complex tori as compact Kähler manifolds with large automorphisms groups.

Holomorphy of Eisenstein series at special points and cohomology of arithmetic subgroups of SLn (Q).

Joachim Schwermer (1986)

Journal für die reine und angewandte Mathematik

How frequent are discrete cyclic subgroups of semisimple Lie groups?

Winkelmann, Jörg (2001)

Documenta Mathematica

Hyperbolic 4-manifolds and conformally flat 3-manifolds

Michael Gromov, H. B. Jr. Lawson, W. Thurston (1988)

Publications Mathématiques de l'IHÉS

Hyperbolic 4-manifolds and tesselations

Nicholaas H. Kuiper (1988)

Publications Mathématiques de l'IHÉS

Hyperbolic geometry and moduli of real cubic surfaces

Daniel Allcock, James A. Carlson, Domingo Toledo (2010)

Annales scientifiques de l'École Normale Supérieure

Let $ℳ_{0}^{ℝ}$ be the moduli space of smooth real cubic surfaces. We show that each of its components admits a real hyperbolic structure. More precisely, one can remove some lower-dimensional geodesic subspaces from a real hyperbolic space $H^{4}$ and form the quotient by an arithmetic group to obtain an orbifold isomorphic to a component of the moduli space. There are five components. For each we describe the corresponding lattices in $PO (4, 1)$ . We also derive several new and several old results on the topology of $ℳ_{0}^{ℝ}$ ....

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