4 citations · 14 across the 20 of their papers we have counts for
22 papers
On local minimality of Hausdorff dimension for round limit sets
Sami Douba, Andrés Sambarino, Franco Vargas Pallete
We address a question of Canary--Taylor and Canary--Minsky--Taylor for sufficiently symmetric compact hyperbolic -orbifolds with totally geodesic boundary. We give sufficient co…
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…
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…
On the stability of Ricci flow on hyperbolic 3-manifolds of finite volume
Ruojing Jiang, Franco Vargas Pallete
On a hyperbolic 3-manifold of finite volume, we prove that if the initial metric is sufficiently close to the hyperbolic metric , then the normalized Ricci-DeTurck flow exists…
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…
W-volume for planar domains with circular boundary
Jeffrey Brock, Franco Vargas Pallete
We extend the notion of Epstein maps to conformal metrics on submanifolds of the unit sphere . Using this construction for curves in $…
Universal Liouville action as a renormalized volume and its gradient flow
Martin Bridgeman, Kenneth Bromberg, Franco Vargas Pallete +1
The universal Liouville action (also known as the Loewner energy for Jordan curves) is a Kähler potential on the Weil-Petersson universal Teichmüller space, which is identified wit…
Cheeger constant of convex co-compact hyperbolic 3-manifolds
Franco Vargas Pallete, Celso Viana
We study the Cheeger isoperimetric constant as a functional in the space of convex co-compact hyperbolic 3-manifolds which are either quasi-Fuchsian or acylindrical. We prove that…
On the topology and index of minimal/Bryant framed surfaces
Davi Maximo, Franco Vargas Pallete
We study framed surfaces, which are a class of Euclidean minimal and hyperbolic CMC-1 surfaces that generalize immersed minimal surfaces in and Bryant surfaces. For…
Peripheral birationality for 3-dimensional convex co-compact varieties
Ian Agol, Franco Vargas Pallete
Let be a hyperbolizable -manifold with boundary, and let be a component of the -character variety of that contains the convex co-compact charac…
Besse projective spaces with many diameters
Ian Adelstein, Franco Vargas Pallete
It is known that Blaschke manifolds (where injectivity radius equals diameter) are Besse manifolds (where all geodesics are closed). We show that Besse manifolds with sufficiently…
The extremal length systole of the Bolza surface
Maxime Fortier Bourque, Dídac Martínez-Granado, Franco Vargas Pallete
We prove that the extremal length systole of genus two surfaces attains a strict local maximum at the Bolza surface, where it takes the value .
Mean curvature flow in homology and foliations of hyperbolic -manifolds
Marco A. M. Guaraco, Vanderson Lima, Franco Vargas Pallete
We study global aspects of the mean curvature flow of non-separating hypersurfaces in closed manifolds. For instance, if has non-vanishing mean curvature, we show its level…
Isoperimetric interpretation for the renormalized volume of convex co-compact hyperbolic 3-manifolds
Franco Vargas Pallete, Celso Viana
We reinterpret the renormalized volume as the asymptotic difference of the isoperimetric profiles for convex co-compact hyperbolic 3-manifolds. By similar techniques we also prove…
Minimal area surfaces and fibered hyperbolic -manifolds
James Farre, Franco Vargas Pallete
By work of Uhlenbeck, the largest principal curvature of any least area fiber of a hyperbolic -manifold fibering over the circle is bounded below by one. We give a short argumen…
Comparing hyperbolic and extremal lengths for shortest curves
Dídac Martínez-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…
A differential form approach to the genus of Open Riemann surfaces
Franco Vargas Pallete, Jesus Zapata Samanez
We will show that any open Riemann surface of finite genus is biholomorphic to an open set of a compact Riemann surface. Moreover, we will introduce a quotient space of forms i…
Embedded Delaunay triangulations for point clouds of surfaces in
Franco Vargas Pallete
In the following article we discuss Delaunay triangulations for a point cloud on an embedded surface in . We give sufficient conditions on the point cloud to show tha…
Additive continuity of the renormalized volume under geometric limits
Franco Vargas Pallete
We study the infimum of the renormalized volume for convex-cocompact hyperbolic manifolds, as well as describing how a sequence converging to such values behaves. In particular, we…
Continuity of the renormalized volume under geometric limits
Franco Vargas Pallete
We extend the concept of renormalized volume for geometrically finite hyperbolic -manifolds, and show that is continuous for geometrically convergent sequences of hyperbolic str…
Local convexity of renormalized volume for rank-1 cusped manifolds
Franco Vargas Pallete
We study the critical points of the renormalized volume for acylindrical geometrically finite hyperbolic 3-manifolds that include rank-1 cusps, and show that the renormalized volum…