Andrew Zimmer
Assistant Professor
Department of Mathematics
University of Wisconsin-Madison
Office: 611 Van Vleck
e-mail: amzimmer2[at]wisc.edu
[ cv | research | teaching | mentoring ]
Research:
I enjoy thinking about geometric problems in several complex variables and discrete subgroups of Lie groups.
Publications / Preprints:
Papers by area: all , several complex variables , discrete subgroups of Lie groups , Riemannian geometry , . . .
The papers below are listed by the year they were made publicly available.
2021:
Hankel operators on domains with bounded intrinsic geometry .
Submitted.
Convex co-compact groups with one dimensional boundary faces (with M. Islam ).
Submitted.
Cusped Hitchin representations and Anosov representations of geometrically finite Fuchsian groups (with R. Canary , T. Zhang ).
Submitted.
2020:
Convex co-compact representations of 3-manifold groups (with M. Islam ).
Submitted.
Compactness of the dbar-Neumann problem on domains with bounded intrinsic geometry .
Journal of Functional Analysis , 2021.
Kobayashi hyperbolic convex domains not biholomorphic to bounded convex domains .
Mathematische Zeitschrift , to appear.
A lower bound for the K\"ahler-Einstein distance from the Diederich-Fornaess index .
Proceedings of the AMS , 2021.
The space of convex domains in complex Euclidean space (with H. Gaussier ).
Journal of Geometric Analysis (special issue), 2020.
Expository.
A higher rank rigidity theorem for convex real projective manifolds .
Submitted.
2019:
Convex co-compact actions of relatively hyperbolic groups (with M. Islam ).
Geometry and Topology , to appear.
Smoothly bounded domains covering compact manifolds .
Submitted.
A flat torus theorem for convex co-compact actions of projective linear
groups (with M. Islam ).
Journal of the London Math. Society , 2021.
Subelliptic estimates from Gromov hyperbolicity .
Submitted.
Regularity of limit sets of Anosov representations (with T. Zhang ).
Submitted.
2018:
The geometry of domains with negatively pinched K\"ahler metrics (with F. Bracci , H. Gaussier ).
Submitted.
Asymptotic behavior of orbits of holomorphic semigroups (with
F. Bracci ,
M. Contrears ,
S. Diaz-Madrigal ,
H. Gaussier ).
Journal de Mathématiques Pures et Appliquées , 2020.
Two boundary rigidity results for holomorphic maps .
American Journal of Mathematics , to appear.
Homeomorphic extension of quasi-isometries for convex domains in C^d and iteration theory (with F. Bracci , H. Gaussier ).
Mathematische Annalen , 2021.
Smoothly bounded domains covering finite volume manifolds .
Journal of Differential Geometry , 2021.
2017:
The automorphism group and limit set of a bounded domain II: the convex case .
Journal of the London Math. Society , 2021.
The automorphism group and limit set of a bounded domain I: the finite type case .
Advances in Mathematics , 2020.
Projective Anosov representations, convex cocompact actions, and rigidity .
Journal of Differential Geometry , to appear.
Characterizing strong pseudoconvexity, obstructions to biholomorphisms, and Lyapunov exponents .
Mathematische Annalen , 2019.
2016:
A gap theorem for the complex geometry of convex domains .
Transactions of the AMS , 2018.
Generic analytic polyhedron with non-compact automorphism group .
Indiana University Mathematics Journal , 2018.
Gromov Hyperbolicity of Bounded Convex Domains .
In: Blanc-Centi, editor, Metrical and dynamical aspects of complex analysis , pp. 67-114
Lecture Notes in Mathematics, Vol. 2195, New York: Springer, 2017.
Goldilocks domains, a weak notion of visibility, and applications
(with G. Bharali ).
Advances in Mathematics , 2017.
2015:
Rigidity of convex divisible domains in flag manifolds
(with W. Van Limbeek ).
Geometry and Topology , 2019.
Entropy rigidity of Hilbert and Riemannian metrics
(with
T. Barthelmé ,
L. Marquis ).
International Mathematics Research Notices , 2017.
Proper quasi-homogeneous domains in flag manifolds and geometric
structures .
Annales de l'Institut Fourier , 2018.
Characterizing the unit ball by its projective automorphism group .
Geometry and Topology , 2016.
The structure of projective maps between real projective manifolds .
Geometriae Dedicata , 2017.
Characterizing domains by the limit set of their automorphism group .
Advances in Mathematics , 2017.
An earlier version was titled: Characterizing polynomial domains by their automorphism group.
2014 and before:
Gromov hyperbolicity, the Kobayashi metric, and C-convex sets .
Transactions of the AMS , 2017.
Gromov hyperbolicity and the Kobayashi metric on convex domains of finite type .
Mathematische Annalen , 2016.
Rigidity of complex convex divisible sets .
Journal of Topology and Analysis , 2018.
Boundaries of non-compact harmonic manifolds .
Geometriae Dedicata , 2014.
Compact asymptotically harmonic manifolds .
Journal of Modern Dynamics , 2012.
A symplectic proof of a theorem of Franks (with
B. Collier ,
E. Kerman ,
B. Reiniger, B. Turmunk).
Compositio Mathematica , 2012.
I also have some undergraduate publications.
Other manuscripts:
Videos:
Last updated: October 10, 2021.