9 papers
Bordered hyperbolic manifolds with a fixed perimeter-to-volume ratio
Sami Douba, Franco Vargas Pallete
We exhibit, for any , infinitely many pairwise incommensurable complete finite-volume hyperbolic -manifolds, both compact and noncompact, each with nonempty totally ge…
Existence of Minimal Surfaces in Infinite Volume Hyperbolic 3-manifolds
Baris Coskunuzer, Zheng Huang, Ben Lowe +1
The existence of embedded minimal surfaces in non-compact 3-manifolds remains a largely unresolved and challenging problem in geometry. In this paper, we address several open cases…
Epstein curves and holography of the Schwarzian action
Franco Vargas Pallete, Yilin Wang, Catherine Wolfram
We apply Epstein's construction of hypersurfaces in the hyperbolic disk to prove identities between the Schwarzian action on $\operatorname{PSL}_2(\mathbb R)\backslash…
Comparing hyperbolic and extremal lengths for shortest curves
DÃdac MartÃnez-Granado, Franco Vargas Pallete
We give a lower bound for the widths of the collars of certain short partial pants decomposition of the surface. Then we apply this to obtain upper bounds of the renormalized volum…
Volume comparison on finite-volume hyperbolic 3-manifolds
Ruojing Jiang, Franco Vargas Pallete
On finite-volume hyperbolic -manifolds, we compare volumes of different metrics using the exponential convergence of Ricci-DeTurck flow toward the hyperbolic metric . We pr…
Minimal surface entropy and applications of Ricci flow on finite-volume hyperbolic 3-manifolds
Ruojing Jiang, Franco Vargas Pallete
This paper studies minimal surface entropy (the exponential asymptotic growth of the number of minimal surfaces up to a given value of area) for negatively curved metrics on hyperb…