On the classification of Cartan actions (2009)
Abstract. We study higher rank Cartan actions on compact manifolds preserving an ergodic measure with full support. In particular, we classify actions by R k with k ≥ 3 whose one-parameter groups...
REGULARITY OF CONJUGACIES OF ALGEBRAIC ACTIONS OF ZARISKI DENSE GROUPS (2009)
Alexander Gorodnik, Theron Hitchman, Ralf Spatzier
Abstract. Let α0 be an affine action of a discrete group Γ on a compact homogeneous space X and α1 a smooth action of Γ on X which is C 1-close to α0. We show that under some conditions, every...
Totally non-symplectic Anosov actions on tori and nilmanifolds (2009)
Fisher, David, Kalinin, Boris, Spatzier, Ralf
We show that sufficiently irreducible totally non-symplectic Anosov actions of higher rank abelian groups on tori and nilmanifolds are $\ci$-conjugate to affine actions.
Regularity of conjugacies of algebraic actions of Zariski dense groups (2008)
Gorodnik, Alexander, Hitchman, Theron, Spatzier, Ralf
Let \alpha_0 be an affine action of a discrete group \Gamma on a compact homogeneous space X and \alpha_1 a smooth action of \Gamma on X which is C^1-close to \alpha_0. We show that under some...
Abstract. We investigate rigidity of measurable structure for higher rank abelian algebraic actions. In particular, we show that ergodic measures for these actions fiber over a 0 entropy measure with...
On the Classification of Cartan Actions (2004)
Kalinin, Boris, Spatzier, Ralf
We study higher rank Cartan actions on compact manifolds preserving an ergodic measure with full support. In particular, we classify actions by $\R ^k$ with $k \geq 3$ whose one-parameter groups act...
Spherical rank rigidity and Blaschke manifolds (2003)
Shankar, Krishnan, Spatzier, Ralf, Wilking, Burkhard
Let M be a complete Riemannian manifold whose sectional curvature is bounded above by 1. We say that M has positive spherical rank if along every geodesic one hits a conjugate point at t=\pi. The...
Rigidity of the measurable structure for algebraic actions of higher rank abelian groups (2002)
Kalinin, Boris, Spatzier, Ralf
We investigate rigidity of measurable structure for higher rank abelian algebraic actions. In particular, we show that ergodic measures for these actions fiber over a 0 entropy measure with Haar...
Manifolds of nonpositive curvature and their buildings (1987)
Let M be a complete Riemannian manifold of bounded nonpositive sectional curvature and finite volume. We construct a topological Tits building A(~I) associated to the universal cover of M. If IV [ is...