Publications – Ralf Spatzier

Cartan actions of higher rank abelian groups and their classification,
with K. Vinhage
Journal of the American Mathematical Society, 37 (3), 2024, 731–859
https://doi.org/10.1090/jams/1033.

Anatole Katok’s work on cohomology and geometric rigidity,
The Collected Works of Anatole Katok vol. II, 2024.

Carnot metrics, dynamics and local rigidity,
with Chris Connell and Thang Nguyen
Ergodic Theory Dynam. Systems, 42(2):614–664, 2022.

Almost Isotropic Kaehler Manifolds
with B. Schmidt and K. Shankar
J. Reine Angew. Math., 767 (2020), 1–16.

Hyperbolic rank rigidity for manifolds of 1/4-pinched negative curvature
with C. Connell and T. Nguyen
Ergodic Theory and Dynamical Systems, 40(5), 1194-1216, 2018.

Smooth Factors of Projective Actions of Higher Rank Lattices and Rigidity
with A. Gorodnik
Geometry and Topology 22 (2018), 1227-1266.

Character Varieties and Actions on Products of Trees
with D. Fisher, M. Larsen and M. Stover
Israel Journal of Mathematics 225 (2018), 889–907.

Exponential Mixing and Smooth Classification of Commuting Expanding Maps
with L. Yang
Journal of Modern Dynamics 11 (2017), 263-312.

Equilibrium Measures for Certain Isometric Extensions of Anosov Systems
with D. Visscher
Ergodic Theory and Dynamical Systems,
Published online: 22 September 2016, pp. 1-14. doi: 10.1017/etds.2016.62.

On the Work of Rodriguez Hertz on Rigidity in Dynamical Systems
Journal of Modern Dynamics 10 (2016), 191-207.

Positively Curved Manifolds With Large Spherical Rank
with B. Schmidt and K. Shankar
Commentarii Mathematici Helvetici 91 (2) (2016), 219-251.

Affine Maps Between CAT(0) Spaces
with H. Bennett and C. Mooney
Geometriae Dedicata 180 (2016), 1-16

Mixing Properties of Commuting Nilmanifold Automorphisms
with A. Gorodnik
Acta Mathematica 215 (1) (2015), 127-159

Exponential Mixing of Nilmanifold Automorphisms
with A. Gorodnik
Journal d’Analyse, 123 (2014), 355-396.

Global Rigidity of Higher Rank Anosov Actions on Tori and Nilmanifolds
with D. Fisher and B. Kalinin
Journal of the American Mathematical Society 26 (2013), 167-198.

Totally non-symplectic Anosov actions on Tori and Nilmanifolds
with D. Fisher and B. Kalinin
Geometry & Topology 15 (2011), 191-216.

Regularity of conjugacies of algebraic actions of Zariski dense groups
with A. Gorodnik and T. J. Hitchman
J. Mod. Dyn. 2 (2008), no. 3, 509-540.

On the Classification of Cartan Actions
with B. Kalinin
GAFA v. 17 (2007), p. 468-490.

Spherical rank rigidity and Blaschke manifolds
with K. Shankar and B. Wilking
Duke J. Math. v. 128, 2005

Measurable rigidity for higher rank abelian actions
with B. Kalinin
Ergodic Th. and Dynam. Systems, v. 25, 2005, p. 175-200

An Invitation to Rigidity Theory
in: Modern Dynamical Systems and Applications (ed. M. Brin, B. Hasselblatt, Y. Pesin),
p. 211-231, Cambridge University Press 2004.

Smooth classification of Cartan actions of higher rank semisimple Lie groups and their lattices
with E. Goetze
Annals of Mathematics, 150 (1999), 743–773.

Differential Rigidity of Anosov Actions of Higher Rank Abelian Groups and Algebraic Lattice Actions
with A. Katok
Dynamical systems and related topics, Proceedings of Steklov Math. Institute, v. 216, 1997, 287–314,
(Editors A.A.Bolibruch, A.M. Stepin, V.V.Ryzhikov).

On Livsic’s theorem, superrigidity, and Anosov actions of semisimple Lie groups
with E. Goetze
Duke Math. J. 88 (1997), 1–27.

Non-stationary normal forms and rigidity of group actions
with A. Katok
Elect. Res. Ann. of the AMS 2 (1996), no. 3, 124-133.

Invariant measures for higher rank hyperbolic Abelian actions
with A. Katok
Ergod. Th. and Dynam. Syst. 16 (1996), 751–778
Corrections (PDF file).

Harmonic analysis in rigidity theory
Ergodic Theory and Its Connections With Harmonic Analysis, (Alexandria 1993), 153–205,
London Math. Soc. Lecture Note Ser. 205, Cambridge University Press, Cambridge, 1995.

First Cohomology of Anosov Actions of Higher Rank Abelian Groups And Applications to Rigidity
with A. Katok
Publ. Math. IHES. 79 (1994), 131–156.
Errata (PDF file)

New examples of manifolds with completely integrable geodesic flows
with G. Paternain
Advances in Math. 108, (1994), 346–366.

Subelliptic estimates of polynomial differential operators and applications to rigidity of Abelian actions
with A. Katok
Math. Res. Letters 1 (1994), 1–11.

Riemannian manifolds with completely integrable geodesic flows
Proc. Symp. Pure Math. 54 (1993), Part 3,
(ed. R. E. Greene, S.-T. Yau), 599–608.

Fundamental groups of negatively curved manifolds and actions of semisimple groups
with R. J. Zimmer
Topology 30 (1991), 591–601.

Some examples of higher rank manifolds of nonnegative curvature
with M. Strake
Comment. Math. Helv. 65 (1990), 299–317.

Geometrically Finite Groups, Patterson-Sullivan measures and Ratner’s theorem
with L. Flaminio
Invent. Math. 99 (1990), 601–626.

Kazhdan groups, cocycles and trees
with S. Adams
Amer. J. of Math. 112 (1990), 271–287.

On isospectral locally symmetric spaces and a theorem of von Neumann
Duke Math. J. 59 (1989), 289–294.
Correction Duke Math. J. 60 (1990), 561

Ratner’s rigidity theorem for geometrically finite groups
with L. Flaminio
in: J. C. Alexander (ed.), Dynamical Systems, Proceedings, (University of Maryland, 1986/87),
Lecture Notes in Mathematics 1342, 180–195.

Infinite Coxeter groups do not have Kazhdan’s property
with M. Bozejko and T. Januszkiewicz
J. of Operator Theory 19 (1988), 63–67.

An example of an amenable action from geometry
Ergod. Th. & Dynam. Syst. 7 (1987), 289–293.

Manifolds of nonpositive curvature and their buildings
(with K. Burns)
Publ. Math. IHES 65 (1987), 35–59.

On topological Tits buildings and their classification
with K. Burns
Publ. Math. IHES 65 (1987), 5–34.

Structure of manifolds of nonpositive curvature II
with W. Ballmann and M. Brin
Annals of Math. 122 (1985), 204–234.

Lattices acting on boundaries of semisimple groups
Ergod. Th. and Dynam. Syst. 1 (1981), 489–494.

Dynamical Properties of Algebraic Systems
Ph.D. Thesis, University of Warwick 1983.