Geodesic
Uniform spectral gap and orthogeodesic counting for strong convergence of Kleinian groups
Forum of Mathematics, Sigma, Tome 11 (2023)

Voir la notice de l'article provenant de la source Cambridge University Press

We show convergence of small eigenvalues for geometrically finite hyperbolic n-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. 
@article{10_1017_fms_2023_64,
     author = {Beibei Liu and Franco Vargas Pallete},
     title = {Uniform spectral gap and orthogeodesic counting for strong convergence of {Kleinian} groups},
     journal = {Forum of Mathematics, Sigma},
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     year = {2023},
     doi = {10.1017/fms.2023.64},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.64/}
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Beibei Liu; Franco Vargas Pallete. Uniform spectral gap and orthogeodesic counting for strong convergence of Kleinian groups. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.64

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