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Geodesic planes in hyperbolic 3-manifolds
- C. McMullen, A. Mohammadi, H. Oh
- Mathematics
- 1 August 2017
This paper initiates the study of rigidity for immersed, totally geodesic planes in hyperbolic 3-manifolds M of infinite volume. In the case of an acylindrical 3-manifold whose convex core has…
On uniform exponential growth for linear groups
Let Γ be a finitely generated group. Given a finite set of generators S of Γ, the word length lS(γ) for an element γ ∈ Γ is defined to be the smallest positive integer for which there exist s1, · · ·…
Orbit closures of unipotent flows for hyperbolic manifolds with Fuchsian ends
- Minju M. Lee, H. Oh
- Mathematics
- 18 February 2019
We establish an analogue of Ratner's orbit closure theorem for any connected closed subgroup generated by unipotent elements in $\operatorname{SO}(d,1)$ acting on the space $\Gamma\backslash…
Apollonian circle packings and closed horospheres on hyperbolic 3-manifolds
- Alex Kontorovich, H. Oh
- Mathematics
- 14 November 2008
We obtain an asymptotic formula for the number of circles of curvature at most T in any given bounded Apollonian circle packing. For an integral packing, we obtain the upper bounds for the number of…
Equidistribution and counting for orbits of geometrically finite hyperbolic groups
Let G be the identity component of SO(n,1), acting linearly on a finite dimensional real vector space V. Consider a vector w_0 in V such that the stabilizer of w_0 is a symmetric subgroup of G or the…
Horocycles in hyperbolic 3-manifolds
- C. McMullen, A. Mohammadi, H. Oh
- Mathematics
- 30 July 2016
Uniform pointwise bounds for matrix coefficients of unitary representations and applications to Kazhdan constants
- H. Oh
- Mathematics
- 15 May 2002
Let k be a local field and G the group of k-rational points of a connected reductive linear algebraic group over k with k-semisimple rank(G) ≥ 2. Let K be a good maximal compact subgroup of G. For a…
Manin's and Peyre's conjectures on rational points and adelic mixing
- A. Gorodnik, F. Maucourant, H. Oh
- Mathematics
- 6 January 2006
Let X be the wonderful compactification of a connected adjoint semisimple
group G defined over a number field K. We prove Manin’s conjecture on the
asymptotic (as T → ∞) of the number of K-rational…
Matrix coefficients, counting and primes for orbits of geometrically finite groups
- A. Mohammadi, H. Oh
- MathematicsJournal of the European Mathematical Society
- 20 August 2012
Let G:=SO(n,1)^\circ and \Gamma be a geometrically finite Zariski dense subgroup with critical exponent delta bigger than (n-1)/2. Under a spectral gap hypothesis on L^2(\Gamma \ G), which is always…
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