24 citations · 96 across the 28 of their papers we have counts for
46 papers
Patterson-Sullivan measures for relatively Anosov groups
Richard Canary, Andrew Zimmer, Tengren Zhang
We establish existence, uniqueness and ergodicity results for Patterson-Sullivan measures for relatively Anosov groups. As applications we obtain an entropy gap theorem and a stric…
A rigidity result for proper holomorphic maps between balls
Edgar Gevorgyan, Haoran Wang, Andrew Zimmer
In this note, we prove a rigidity result for proper holomorphic maps between unit balls that have many symmetries and which extend to -smooth maps on the boundary.
Patterson-Sullivan measures for transverse subgroups
Richard Canary, Tengren Zhang, Andrew Zimmer
We study Patterson-Sullivan measures for a class of discrete subgroups of higher rank semisimple Lie groups, called transverse groups, whose limit set is well-defined and transvers…
Relatively Anosov representations via flows II: examples
Feng Zhu, Andrew Zimmer
This is the second in a series of two papers that develops a theory of relatively Anosov representations using the original "contracting flow on a bundle" definition of Anosov repr…
Relatively Anosov representations via flows I: theory
Feng Zhu, Andrew Zimmer
This is the first in a series of two papers that develops a theory of relatively Anosov representations using the original "contracting flow on a bundle" definition of Anosov repre…
Unbounded visibility domains, the end compactification, and applications
Gautam Bharali, Andrew Zimmer
In this paper we study when the Kobayashi distance on a Kobayashi hyperbolic domain has certain visibility properties, with a focus on unbounded domains. "Visibility" in this conte…
Entropy rigidity for cusped Hitchin representations
Richard Canary, Tengren Zhang, Andrew Zimmer
We establish an entropy rigidity theorem for Hitchin representations of all geometrically finite Fuchsian groups which generalizes a theorem of Potrie and Sambarino for Hitchin rep…
A metric analogue of Hartogs' theorem
Hervé Gaussier, Andrew Zimmer
In this paper we prove a metric version of Hartogs' theorem where the holomorphic function is replaced by a locally symmetric Hermitian metric. As an application, we prove that if…
Hankel operators on domains with bounded intrinsic geometry
Andrew Zimmer
In this paper we consider Hankel operators on domains with bounded intrinsic geometry. For these domains we characterize the -symbols where the associated Hankel operator is c…
Convex co-compact groups with one dimensional boundary faces
Mitul Islam, Andrew Zimmer
In this paper we consider convex co-compact subgroups of the projective linear group. We prove that such a group is relatively hyperbolic with respect to a collection of virtually…
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…
Compactness of the -Neumann problem on domains with bounded intrinsic geometry
Andrew Zimmer
By considering intrinsic geometric conditions, we introduce a new class of domains in complex Euclidean space. This class is invariant under biholomorphism and includes strongly ps…
Convex co-compact representations of 3-manifold groups
Mitul Islam, Andrew Zimmer
A representation of a finitely generated group into the projective general linear group is called convex co-compact if it has finite kernel and its image acts convex co-compactly o…
Kobayashi hyperbolic convex domains not biholomorphic to bounded convex domains
Andrew Zimmer
We construct families of convex domains that are biholomorphic to bounded domains, but not bounded convex domains. This is accomplished by finding an obstruction related to the Gro…
A lower bound for the Kähler-Einstein distance from the Diederich-Fornæss index
Andrew Zimmer
In this note we establish a lower bound for the distance induced by the Kähler-Einstein metric on pseudoconvex domains with positive hyperconvexity index (e.g. positive Diederich-F…
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.
Smoothly bounded domains covering compact manifolds
Andrew Zimmer
We show that if a bounded domain in complex Euclidean space with boundary covers a compact manifold, then the domain is biholomorphic to the unit ball.
Convex co-compact actions of relatively hyperbolic groups
Mitul Islam, Andrew Zimmer
In this paper we consider discrete groups in acting convex co-compactly on a properly convex domain in real projective space. For such groups, we establis…
A flat torus theorem for convex co-compact actions of projective linear groups
Mitul Islam, Andrew Zimmer
In this paper, we consider discrete groups in acting convex co-compactly on a properly convex domain in real projective space. For such groups, we establi…
Subelliptic estimates from Gromov hyperbolicity
Andrew Zimmer
In this paper we prove: if the complete Kähler-Einstein metric on a bounded convex domain (with no boundary regularity assumptions) is Gromov hyperbolic, then the -…
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…
Two boundary rigidity results for holomorphic maps
Andrew Zimmer
In this paper we establish two boundary versions of the Schwarz lemma. The first is for general holomorphic self maps of bounded convex domains with boundary. This appears to…
Asymptotic behavior of orbits of holomorphic semigroups
Filippo Bracci, Manuel D. Contreras, Santiago Díaz-Madrigal +2
Let be a holomorphic semigroup of the unit disc (i.e., the flow of a semicomplete holomorphic vector field) without fixed points in the unit disc and let be the starlik…
The geometry of domains with negatively pinched Kähler metrics
Filippo Bracci, Hervé Gaussier, Andrew Zimmer
We study how the existence of a negatively pinched Kähler metric on a domain in complex Euclidean space restricts the geometry of its boundary. In particular, we show that if a con…