Franco Vargas Pallete

activity

20192022

collaborators

4 papers

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 $n$ -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.GT2020

Hyperbolic limits of Cantor set complements in the sphere

Tommaso Cremaschi, Franco Vargas Pallete

Let $M$ be a hyperbolic 3-manifold with no rank two cusps admitting an embedding in $S^{3}$ . Then, if $M$ admits an exhaustion by $π_{1}$ -injective sub-manifolds there exists c…

math.DG2019

Upper bounds on Renormalized Volume for Schottky groups

Franco Vargas Pallete

In this article we show that for any given Riemann surface $Σ$ of genus $g$ , we can bound (from above) the renormalized volume of a (hyperbolic) Schottky group with boundary at inf…