Andrew Zimmer
Associate Professor
Department of Mathematics
University of Wisconsin-Madison
Office: 611 Van Vleck
e-mail: amzimmer2[at]wisc.edu
[ cv | research | 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 .
The papers below are listed by the year they were made publicly available.
2024:
Counting, mixing and equidistribution for GPS systems with applications to relatively Anosov groups (with P.-L. Blayac , R. Canary , F. Zhu ).
Preprint, 55 pages.
Patterson-Sullivan theory for coarse cocycles (with P.-L. Blayac , R. Canary , F. Zhu ).
Preprint, 66 pages.
2023:
Smooth equivalence of families of strongly pseudoconvex domains (with H. Gaussier , X. Gong ).
Submitted, 31 pages.
Patterson-Sullivan measures for relatively Anosov groups (with R. Canary , T. Zhang ).
Submitted, 40 pages.
A rigidity result for proper holomorphic maps between balls (with E. Gevorgyan, H. Wang).
Proceedings of the AMS , 152:1573-1585, 2024.
REU Project!
Patterson-Sullivan measures for transverse subgroups (with R. Canary , T. Zhang ).
Journal of Modern Dynamics , to appear, 46 pages.
2022:
Relatively Anosov representations via flows II: examples
(with F. Zhu ).
Submitted, 51 pages.
Relatively Anosov representations via flows I: theory
(with F. Zhu ).
Submitted, 67 pages.
Unbounded visibility domains, the end compactification, and applications
(with G. Bharali ).
Transactions of the AMS , 376: 5949-5988, 2023.
The structure of relatively hyperbolic groups in convex real projective geometry (with M. Islam ).
Submitted, 30 pages.
Entropy rigidity for cusped Hitchin representations (with R. Canary , T. Zhang ).
Submitted, 57 pages.
2021:
A metric analogue of Hartogs' theorem (with H. Gaussier ).
Geometric and Functional Analysis , 32: 1041-1062, 2022.
An earlier version was titled: When is the Kobayashi metric a K\"ahler metric?
Hankel operators on domains with bounded intrinsic geometry .
Journal of Geometric Analysis , 33: Article number: 176, 2023 (29 pages).
Convex co-compact groups with one dimensional boundary faces (with M. Islam ).
Submitted, 24 pages.
Cusped Hitchin representations and Anosov representations of geometrically finite Fuchsian groups (with R. Canary , T. Zhang ).
Advances in Mathematics , 404, Part B: 108439, 2022 (67 pages).
2020:
Convex co-compact representations of 3-manifold groups (with M. Islam ).
Journal of Topology , to appear, 48 pages.
Compactness of the dbar-Neumann problem on domains with bounded intrinsic geometry .
Journal of Functional Analysis , 281: 108992, 2021 (47 pages).
Kobayashi hyperbolic convex domains not biholomorphic to bounded convex domains .
Mathematische Zeitschrift , 300: 1905-1916, 2022.
A lower bound for the K\"ahler-Einstein distance from the Diederich-Fornaess index .
Proceedings of the AMS , 149: 1641-1646, 2021.
The space of convex domains in complex Euclidean space (with H. Gaussier ).
Journal of Geometric Analysis (special issue), 30: 1312-1358, 2020.
Expository.
A higher rank rigidity theorem for convex real projective manifolds .
Geometry and Topology , 27: 2899-2936, 2023.
2019:
Convex co-compact actions of relatively hyperbolic groups (with M. Islam ).
Geometry and Topology , 27: 417-511, 2023.
Smoothly bounded domains covering compact manifolds .
Indiana University Mathematics Journal , 70: 2653-2676, 2021.
A flat torus theorem for convex co-compact actions of projective linear
groups (with M. Islam ).
Journal of the London Math. Society , 103: 470-489, 2021.
Subelliptic estimates from Gromov hyperbolicity .
Advances in Mathematics , 402: 108334, 2022 (94 pages).
Regularity of limit sets of Anosov representations (with T. Zhang ).
Submitted, 58 pages.
2018:
The geometry of domains with negatively pinched K\"ahler metrics (with F. Bracci , H. Gaussier ).
Journal of Differential Geometry , to appear, 26 pages.
Asymptotic behavior of orbits of holomorphic semigroups (with
F. Bracci ,
M. Contrears ,
S. Diaz-Madrigal ,
H. Gaussier ).
Journal de Mathématiques Pures et Appliquées , 133: 263-286, 2020.
Two boundary rigidity results for holomorphic maps .
American Journal of Mathematics , 144: 119-168, 2022.
Homeomorphic extension of quasi-isometries for convex domains in C^d and iteration theory (with F. Bracci , H. Gaussier ).
Mathematische Annalen , 379: 691-718, 2021.
Smoothly bounded domains covering finite volume manifolds .
Journal of Differential Geometry , 119: 161-182, 2021.
2017:
The automorphism group and limit set of a bounded domain II: the convex case .
Journal of the London Math. Society , 104: 453-491, 2021.
The automorphism group and limit set of a bounded domain I: the finite type case .
Advances in Mathematics , 366: 107085, 2020 (42 pages).
Projective Anosov representations, convex cocompact actions, and rigidity .
Journal of Differential Geometry , 119: 513-586, 2021.
Characterizing strong pseudoconvexity, obstructions to biholomorphisms, and Lyapunov exponents .
Mathematische Annalen , 374: 1811-1844, 2019.
2016:
A gap theorem for the complex geometry of convex domains .
Transactions of the AMS , 370: 7489-7509, 2018.
Generic analytic polyhedron with non-compact automorphism group .
Indiana University Mathematics Journal , 67: 1299-1326, 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 , 310: 377-425, 2017.
2015:
Rigidity of convex divisible domains in flag manifolds
(with W. Van Limbeek ).
Geometry and Topology , 23: 171-240, 2019.
Entropy rigidity of Hilbert and Riemannian metrics
(with
T. Barthelmé ,
L. Marquis ).
International Mathematics Research Notices , 2017 (22): 6841-6866, 2017.
Proper quasi-homogeneous domains in flag manifolds and geometric
structures .
Annales de l'Institut Fourier , 68: 2635-2662, 2018.
Characterizing the unit ball by its projective automorphism group .
Geometry and Topology , 20: 2397-2432, 2016.
The structure of projective maps between real projective manifolds .
Geometriae Dedicata , 190: 81-102, 2017.
Characterizing domains by the limit set of their automorphism group .
Advances in Mathematics , 308: 438 - 482, 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 , 369: 8437-8456, 2017.
Gromov hyperbolicity and the Kobayashi metric on convex domains of finite type .
Mathematische Annalen , 365: 1425-1498, 2016.
Rigidity of complex convex divisible sets .
Journal of Topology and Analysis , 10: 817-85, 2018.
Boundaries of non-compact harmonic manifolds .
Geometriae Dedicata , 168: 339-357, 2014.
Compact asymptotically harmonic manifolds .
Journal of Modern Dynamics , 6: 377-403, 2012.
A symplectic proof of a theorem of Franks (with
B. Collier ,
E. Kerman ,
B. Reiniger, B. Turmunk).
Compositio Mathematica , 148: 1969-1984, 2012.
I also have some undergraduate publications.
Other manuscripts:
Videos:
Last updated: April 14, 2024.