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Award ID contains: 2417229

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  1. ; (, Forum of Mathematics, Sigma)
    Abstract We show convergence of small eigenvalues for geometrically finite hyperbolicn-manifolds under strong limits. For a class of convergent convex sets in a strongly convergent sequence of Kleinian groups, we use the spectral gap of the limit manifold and the exponentially mixing property of the geodesic flow along the strongly convergent sequence to find asymptotically uniform counting formulas for the number of orthogeodesics between the convex sets. In particular, this provides asymptotically uniform counting formulas (with respect to length) for orthogeodesics between converging Margulis tubes, geodesic loops based at converging basepoints, and primitive closed geodesics. 
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  2. ; (, Forum of Mathematics, Sigma)
    Abstract We study the Eisenstein series associated to the full rank cusps in a complete hyperbolic manifold. We show that given a Kleinian group$$\Gamma <{\operatorname{\mathrm{Isom}}}^+(\mathbb H^{n+1})$$, each full rank cusp corresponds to a cohomology class in$$H^{n}(\Gamma , V)$$, whereVis either the trivial coefficient or the adjoint representation. Moreover, by computing the intertwining operator, we show that different cusps give rise to linearly independent classes. 
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  3. ; (, Journal of Differential Geometry)
    Free, publicly-accessible full text available November 1, 2025
  4. ; (, Geometry & Topology)
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