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…
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…
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…
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…