13 citations · 15 across the 6 of their papers we have counts for
9 papers
Strong spectral gap for geometrically finite hyperbolic manifolds
Dubi Kelmer, Osama Khalil, Pratyush Sarkar
Let for be a Zariski dense, geometrically finite, discrete subgroup with critical exponent strictly greater than . We show that…
Exponential Mixing Via Additive Combinatorics
Osama Khalil
We prove that the geodesic flow on a geometrically finite locally symmetric space of negative curvature is exponentially mixing with respect to the Bowen-Margulis-Sullivan measure.…
On the Space of Ergodic Measures for the Horocycle Flow on Strata of Abelian Differentials
Jon Chaika, Osama Khalil, John Smillie
We study the horocycle flow on the stratum of translation surfaces . We show that there is a sequence of horocycle ergodic measures, each supported on a periodic ho…
Random Walks, Spectral Gaps, and Khintchine's Theorem on Fractals
Osama Khalil, Manuel Luethi
This work addresses problems on simultaneous Diophantine approximation on fractals, motivated by a long standing problem of Mahler regarding Cantor's middle set. We obtain th…
Singular Vectors on Fractals and Projections of Self-similar Measures
Osama Khalil
Singular vectors are those for which the quality of rational approximations provided by Dirichlet's Theorem can be improved by arbitrarily small multiplicative constants. We provid…
Bounded and Divergent Trajectories And Expanding Curves on Homogeneous Spaces
Osama Khalil
Suppose is a -parameter -diagonalizable subgroup of a Lie group and is a lattice. We study the dimension of bounded and divergent orbits of e…
Geodesic Planes in Geometrically Finite Manifolds
Osama Khalil
We study the problem of rigidity of closures of totally geodesic plane immersions in geometrically finite manifolds containing rank cusps. We show that the key notion of K-thic…
Exceptional directions for the Teichmüller geodesic flow and Hausdorff dimension
Hamid Al-Saqban, Paul Apisa, Alena Erchenko +3
We prove that for every flat surface , the Hausdorff dimension of the set of directions in which Teichmüller geodesics starting from exhibit a definite amount of deviation f…
Pointwise Equidistribution and Translates of Measures on Homogeneous Spaces
Osama Khalil
Let be a Borel probability space. Let be a sequence of continuous transformations on . Let be a probability measure on such th…