Effective equidistribution of circles in the limit sets of Kleinian groups
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2017, 11: 155-188. doi: 10.3934/jmd.2017008
On the rate of equidistribution of expanding horospheres in finite-volume quotients of SL(2, ${\mathbb{C}}$)
Samuel C. Edwards
Department of Mathematics, Box 480, Uppsala University, SE-75106 Uppsala, Sweden
Received December 22, 2015 Revised December 02, 2016 Published February 2017
Let $\Gamma$ be a lattice in $G=\mathrm{SL}(2, \mathbb{C})$. We give an effective equidistribution result with precise error terms for expanding translates of pieces of horospherical orbits in $\Gamma\backslash G$. Our method of proof relies on the theory of unitary representations.
Keywords: Effective equidistribution, translates, horospheres.
Mathematics Subject Classification: Primary: 37A17; Secondary: 11F03.
Citation: Samuel C. Edwards. On the rate of equidistribution of expanding horospheres in finite-volume quotients of SL(2, ${\mathbb{C}}$). Journal of Modern Dynamics, 2017, 11: 155-188. doi: 10.3934/jmd.2017008
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