24 citations · 96 across the 28 of their papers we have counts for
13 papers · 1 filter
Cusped Hitchin representations and Anosov representations of geometrically finite Fuchsian groups
Richard Canary, Tengren Zhang, Andrew Zimmer
We develop a theory of Anosov representation of geometrically finite Fuchsian groups in SL(d,R) and show that cusped Hitchin representations are Borel Anosov in this sense. We esta…
A higher rank rigidity theorem for convex real projective manifolds
Andrew Zimmer
For convex real projective manifolds we prove an analogue of the higher rank rigidity theorem of Ballmann and Burns-Spatzier.
Regularity of limit sets of Anosov representations
Tengren Zhang, Andrew Zimmer
In this paper we establish necessary and sufficient conditions for the limit set of a projective Anosov representation to be a differentiable submanifold of projective space with H…
Projective Anosov representations, convex cocompact actions, and rigidity
Andrew Zimmer
In this paper we show that many projective Anosov representations act convex cocompactly on some properly convex domain in real projective space. In particular, if a non-elementary…
Rigidity of convex divisible domains in flag manifolds
Wouter van Limbeek, Andrew Zimmer
In contrast to the many examples of convex divisible domains in real projective space, we prove that up to projective isomorphism there is only one convex divisible domain in the G…
Entropy rigidity of Hilbert and Riemannian metrics
Thomas Barthelmé, Ludovic Marquis, Andrew Zimmer
In this paper we provide two new characterizations of real hyperbolic -space using the Poincaré exponent of a discrete group and the volume growth entropy. The first characteriz…
Proper quasi-homogeneous domains in flag manifolds and geometric structures
Andrew Zimmer
In this paper we study domains in flag manifolds which are bounded in an affine chart and whose projective automorphism group acts co-compactly. In contrast to the many examples in…
Characterizing the unit ball by its projective automorphism group
Andrew M. Zimmer
In this paper we study the projective automorphism group of domains in real, complex, and quaternionic projective space and present two new characterizations of the unit ball in te…
The structure of projective maps between real projective manifolds
Andrew Zimmer
In this paper we study the set of projective maps between compact proper convex real projective manifolds. We show that this set contains only finitely many distinct homotopy class…
Rigidity of complex convex divisible sets
Andrew M. Zimmer
An open convex set in real projective space is called divisible if there exists a discrete group of projective automorphisms which acts co-compactly. There are many examples of suc…
Boundaries of non-compact harmonic manifolds
Andrew M. Zimmer
In this paper we consider non-compact non-flat simply connected harmonic manifolds. In particular, we show that the Martin boundary and Busemann boundary coincide for such manifold…
Compact asymptotically harmonic manifolds
Andrew M. Zimmer
A complete Riemannian manifold without conjugate points is called asymptotically harmonic if the mean curvature of its horospheres is a universal constant. Examples of asymptotical…
Asymptotically harmonic manifolds without focal points
Andrew M. Zimmer
In this note we show that a compact asymptotically harmonic manifold without focal points is either flat or a rank one locally symmetric space.