4 papers
Near optimal spectral gaps for line bundles on hyperbolic three-manifolds
Michael Magee, Anna Roig-Sanchis, Joe Thomas
We prove that there exists a sequence of two-torsion Hermitian line bundles on closed hyperbolic three-manifolds, with volume tending to infinity, and with asymptotically optimal s…
The systole of random hyperbolic 3-manifolds
Anna Roig-Sanchis
We study the systole of a model of random hyperbolic 3-manifolds introduced by Petri and Raimbault, answering a question posed in that same article. These are compact manifolds wit…
Minimal surfaces with negative curvature in large dimensional spheres
Michele Ancona, François Labourie, Anna Roig-Sanchis +1
In this note, we answer positively a question of Yau by proving the existence of closed minimal surfaces with negative induced curvature in any sphere of large dimension. The proof…
Apollonian random manifolds and their bass notes
Will Hide, Bram Petri, Anna Roig-Sanchis +1
We study the spectrum of the Laplacian on two models of random hyperbolic 3-orbifolds, related to the Apollonian group and the super Apollonian group. We determine explicit spectra…