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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… Expand

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, · · ·… Expand

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… Expand

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… Expand

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… Expand

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… Expand

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… Expand

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… Expand

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