Michael Kapovich
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Michael Kapovich has a total of 25 co-authors. Here are the top co-authors by number of shared publications:
- Bernhard Leeb
Mathematisches Institut, Universität München, München, Germany
13 shared publications - John J. Millson
Department of Mathematics, University of Maryland, College Park, USA
9 shared publications - Joan Porti
Departament de Matemàtiques, Universitat Autònoma de Barcelona, Cerdanyola del Valles, Spain
7 shared publications - Subhadip Dey
Yale University
7 shared publications - Arkady Berenstein
Department of Mathematics, University of Oregon, Eugene, USA
4 shared publications - Beibei Liu2 shared publications
Latest Publications
- Top Cited PapersOpen Access
- 14 August 2025
- Published by Mathematical Sciences Publishers in Geometry & Topology
- Vol. 29 (5) , 2343-2390
Morse actions of discrete groups on symmetric spaces: local-to-global principle
Our main result is a local-to-global principle for Morse quasigeodesics, maps and actions. As an application of our techniques we show algorithmic recognizability of Morse actions and construct Morse "Schottky subgroups" of higher-rank semisimple Lie groups via arguments not based on Tits pingpong. Our argument is purely geometric and proceeds by constructing equivariant Morse quasiisometric embeddings of trees into higher-rank symmetric spaces.
- 14 August 2025
- Published by Mathematical Sciences Publishers in Geometry & Topology
- Vol. 29 (5) , 2343-2390
Top Cited PapersOpen AccessMorse actions of discrete groups on symmetric spaces: local-to-global principle
Our main result is a local-to-global principle for Morse quasigeodesics, maps and actions. As an application of our techniques we show algorithmic recognizability of Morse actions and construct Morse "Schottky subgroups" of higher-rank semisimple Lie groups via arguments not based on Tits pingpong. Our argument is purely geometric and proceeds by constructing equivariant Morse quasiisometric embeddings of trees into higher-rank symmetric spaces.
- Open Access
Rado's paracompactness theorem for conformal manifolds
We prove that every manifold of dimension $\ge 2$ admitting a conformal structure is paracompact.Open AccessRado's paracompactness theorem for conformal manifolds
We prove that every manifold of dimension $\ge 2$ admitting a conformal structure is paracompact. - Open Access
Examples of aspherical Alexandrov spaces
We construct examples of 3-dimensional compact aspherical Alexandrov spaces without boundary which are not topological manifolds.
Open AccessExamples of aspherical Alexandrov spaces
We construct examples of 3-dimensional compact aspherical Alexandrov spaces without boundary which are not topological manifolds.
- Open Access
- 1 October 2024
- Published by Springer Nature in São Paulo Journal of Mathematical Sciences
- p. 1-18
Correction to: A note on properly discontinuous actions
We correct a mistake appearing in the earlier paper “A note on properly discontinuous actions.”
- 1 October 2024
- Published by Springer Nature in São Paulo Journal of Mathematical Sciences
- p. 1-18
Open AccessCorrection to: A note on properly discontinuous actions
We correct a mistake appearing in the earlier paper “A note on properly discontinuous actions.”
- Open Access
- 24 July 2024
- Published by Springer Nature in Geometriae Dedicata
- Vol. 218 (4) , 1-16
Domains of discontinuity of Lorentzian affine group actions
We prove nonemptyness of domains of proper discontinuity of Anosov groups of affine Lorentzian transformations of $${\mathbb R}^n$$ .- 24 July 2024
- Published by Springer Nature in Geometriae Dedicata
- Vol. 218 (4) , 1-16
Open AccessDomains of discontinuity of Lorentzian affine group actions
We prove nonemptyness of domains of proper discontinuity of Anosov groups of affine Lorentzian transformations of $${\mathbb R}^n$$ . - 1 January 2024
- Published by Institute of Mathematics, Polish Academy of Sciences in Fundamenta Mathematicae
- Vol. 267 (2) , 117-128
Complete characterizations of hyperbolic Coxeter groups with Sierpiński curve boundary and with Menger curve boundary
We give complete characterizations (in terms of nerves) of those word hyperbolic Coxeter groups whose Gromov boundary is homeomorphic to the Sierpiński curve and to the Menger curve, respectively. The justification is mostly an appropriate combination of
- 1 January 2024
- Published by Institute of Mathematics, Polish Academy of Sciences in Fundamenta Mathematicae
- Vol. 267 (2) , 117-128
Complete characterizations of hyperbolic Coxeter groups with Sierpiński curve boundary and with Menger curve boundary
We give complete characterizations (in terms of nerves) of those word hyperbolic Coxeter groups whose Gromov boundary is homeomorphic to the Sierpiński curve and to the Menger curve, respectively. The justification is mostly an appropriate combination of
- Open Access
A note on laminations with symmetric leaves
We prove that (apart from dimension $n=4$), each Riemannian solenoidal lamination with transitive homeomorphism group and leaves isometric to a symmetric space $X$ of noncompact type, is homeomorphic to the inverse limit of the system of finite covers of a compact locally-symmetric $n$-manifold.Open AccessA note on laminations with symmetric leaves
We prove that (apart from dimension $n=4$), each Riemannian solenoidal lamination with transitive homeomorphism group and leaves isometric to a symmetric space $X$ of noncompact type, is homeomorphic to the inverse limit of the system of finite covers of a compact locally-symmetric $n$-manifold. - 28 March 2023
- Published by Walter de Gruyter GmbH in Journal für die reine und angewandte Mathematik (Crelles Journal)
- Vol. 2023 (798) , 105-142
On superintegral Kleinian sphere packings, bugs, and arithmetic groups
We develop the notion of a Kleinian Sphere Packing, a generalization of “crystallographic” (Apollonian-like) sphere packings defined in [A. Kontorovich and K. Nakamura, Geometry and arithmetic of crystallographic sphere packings, Proc. Natl. Acad. Sci. USA 116 2019, 2, 436–441]. Unlike crystallographic packings, Kleinian packings exist in all dimensions, as do “superintegral” such. We extend the Arithmeticity Theorem to Kleinian packings, that is, the superintegral ones come from -arithmetic lattices of simplest type. The same holds for more general objects we call Kleinian Bugs, in which the spheres need not be disjoint but can meet with dihedral angles for finitely many m. We settle two questions from Kontorovich and Nakamura (2019): (i) that the Arithmeticity Theorem is in general false over number fields, and (ii) that integral packings only arise from non-uniform lattices.- 28 March 2023
- Published by Walter de Gruyter GmbH in Journal für die reine und angewandte Mathematik (Crelles Journal)
- Vol. 2023 (798) , 105-142
On superintegral Kleinian sphere packings, bugs, and arithmetic groups
We develop the notion of a Kleinian Sphere Packing, a generalization of “crystallographic” (Apollonian-like) sphere packings defined in [A. Kontorovich and K. Nakamura, Geometry and arithmetic of crystallographic sphere packings, Proc. Natl. Acad. Sci. USA 116 2019, 2, 436–441]. Unlike crystallographic packings, Kleinian packings exist in all dimensions, as do “superintegral” such. We extend the Arithmeticity Theorem to Kleinian packings, that is, the superintegral ones come from -arithmetic lattices of simplest type. The same holds for more general objects we call Kleinian Bugs, in which the spheres need not be disjoint but can meet with dihedral angles for finitely many m. We settle two questions from Kontorovich and Nakamura (2019): (i) that the Arithmeticity Theorem is in general false over number fields, and (ii) that integral packings only arise from non-uniform lattices.- Open Access
- 15 February 2023
- Published by Springer Nature in São Paulo Journal of Mathematical Sciences
- Vol. 18 (2) , 807-836
A note on properly discontinuous actions
We compare various notions of proper discontinuity for group actions. We also discuss fundamental domains and criteria for cocompactness.
- 15 February 2023
- Published by Springer Nature in São Paulo Journal of Mathematical Sciences
- Vol. 18 (2) , 807-836
Open AccessA note on properly discontinuous actions
We compare various notions of proper discontinuity for group actions. We also discuss fundamental domains and criteria for cocompactness.
- Open Access
Relativizing characterizations of Anosov subgroups, I
We propose several common extensions of the classes of Anosov subgroups and geometrically finite Kleinian groups among discrete subgroups of semisimple Lie groups. We relativize various dynamical and coarse geometric characterizations of Anosov subgroups given in our earlier work, extending the class from intrinsically hyperbolic to relatively hyperbolic subgroups. We prove implications and equivalences between the various relativizations.
Open AccessRelativizing characterizations of Anosov subgroups, I
We propose several common extensions of the classes of Anosov subgroups and geometrically finite Kleinian groups among discrete subgroups of semisimple Lie groups. We relativize various dynamical and coarse geometric characterizations of Anosov subgroups given in our earlier work, extending the class from intrinsically hyperbolic to relatively hyperbolic subgroups. We prove implications and equivalences between the various relativizations.