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math.DS2026
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…
math.DS2019
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…
math.DS2018
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…