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math.DG2022
Uniform spectral gap and orthogeodesic counting for strong convergence of Kleinian groups
Beibei Liu, Franco Vargas Pallete
We show convergence of small eigenvalues for geometrically finite hyperbolic -manifolds under strong limits. For a class of convergent convex sets in a strongly convergent seque…
math.DG2020
The length of the shortest closed geodesic on positively curved 2-spheres
Ian Adelstein, Franco Vargas Pallete
We show that the shortest closed geodesic on a 2-sphere with non-negative curvature has length bounded above by three times the diameter. We prove a new isoperimetric inequality fo…
math.DG2019★ 2 cited
Upper bounds on Renormalized Volume for Schottky groups
Franco Vargas Pallete
In this article we show that for any given Riemann surface of genus , we can bound (from above) the renormalized volume of a (hyperbolic) Schottky group with boundary at inf…