Andrew Zimmer

Associate Professor
Department of Mathematics
University of Wisconsin-Madison
Office: 611 Van Vleck
e-mail: amzimmer2[at]wisc.edu

Research:

I enjoy thinking about geometric structures on manifolds, several complex variables, Riemannian geometry, and discrete subgroups of Lie groups.

Publications / Preprints:

Publications in Several Complex Variables:

1. Gromov hyperbolicity of intrinsic metrics from isoperimetric inequalities (with T. Wang).
   Submitted, 44 pages.
2. Smooth equivalence of families of strongly pseudoconvex domains (with H. Gaussier, X. Gong).
   Submitted, 31 pages.
3. A rigidity result for proper holomorphic maps between balls (with E. Gevorgyan, H. Wang).
   Proceedings of the AMS, 152: 1573-1585, 2024.
   REU Project!
4. Unbounded visibility domains, the end compactification, and applications (with G. Bharali).
   Transactions of the AMS, 376: 5949-5988, 2023.
5. A metric analogue of Hartogs' theorem (with H. Gaussier).
   Geometric and Functional Analysis, 32: 1041-1062, 2022.
6. Hankel operators on domains with bounded intrinsic geometry.
   Journal of Geometric Analysis, 33: Article number: 176, 2023 (29 pages).
7. Compactness of the dbar-Neumann problem on domains with bounded intrinsic geometry.
   Journal of Functional Analysis, 281: 108992, 2021 (47 pages).
8. Kobayashi hyperbolic convex domains not biholomorphic to bounded convex domains.
   Mathematische Zeitschrift, 300: 1905-1916, 2022.
9. A lower bound for the K\"ahler-Einstein distance from the Diederich-Fornaess index.
   Proceedings of the AMS, 149: 1641-1646, 2021.
10. Smoothly bounded domains covering compact manifolds.
    Indiana University Mathematics Journal, 70: 2653-2676, 2021.
11. Subelliptic estimates from Gromov hyperbolicity.
    Advances in Mathematics, 402: 108334, 2022 (94 pages).
12. The geometry of domains with negatively pinched K\"ahler metrics (with F. Bracci, H. Gaussier).
    Journal of Differential Geometry, 126: 909-938, 2024.
13. 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.
14. Two boundary rigidity results for holomorphic maps.
    American Journal of Mathematics, 144: 119-168, 2022.
15. Homeomorphic extension of quasi-isometries for convex domains in C^d and iteration theory (with F. Bracci and H. Gaussier).
    Mathematische Annalen, 379: 691-718, 2021.
16. Smoothly bounded domains covering finite volume manifolds.
    Journal of Differential Geometry, 119: 161-182, 2021.
17. The automorphism group and limit set of a bounded domain II: the convex case.
    Journal of the London Math. Society, 104: 453-491, 2021.
18. The automorphism group and limit set of a bounded domain I: the finite type case.
    Advances in Mathematics, 366: 107085, 2020 (42 pages).
19. Characterizing strong pseudoconvexity, obstructions to biholomorphisms, and Lyapunov exponents.
    Mathematische Annalen, 374: 1811-1844, 2019.
20. A gap theorem for the complex geometry of convex domains.
    Transactions of the AMS, 370: 7489-7509, 2018.
21. Generic analytic polyhedron with non-compact automorphism group.
    Indiana University Mathematics Journal, 67 (3): 1299-1326, 2018.
22. 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.
23. Goldilocks domains, a weak notion of visibility, and applications (with G. Bharali).
    Advances in Mathematics, 310: 377-425, 2017.
24. Characterizing domains by the limit set of their automorphism group.
    Advances in Mathematics, 308: 438-482, 2017.
25. Gromov hyperbolicity, the Kobayashi metric, and C-convex sets.
    Transactions of the AMS, 369: 8437-8456, 2017.
26. Gromov hyperbolicity and the Kobayashi metric on convex domains of finite type.
    Mathematische Annalen, 365: 1425-1498, 2016.

Last updated: November 19, 2024.