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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 .
A divergent horocycle in the horofunction compactification of the Teichmüller metric
Maxime Fortier Bourque
We give an example of a horocycle in the Teichmüller space of the five-times-punctured sphere that does not converge in the Gardiner--Masur compactification, or equivalently in the…
Kissing numbers of closed hyperbolic manifolds
Maxime Fortier Bourque, Bram Petri
We prove an upper bound for the number of shortest closed geodesics in a closed hyperbolic manifold of any dimension in terms of its volume and systole, generalizing a theorem of P…
Hyperbolic surfaces with sublinearly many systoles that fill
Maxime Fortier Bourque
For any , we construct a closed hyperbolic surface of genus with a set of at most systoles that fill, meaning that each component…
Local maxima of the systole function
Maxime Fortier Bourque, Kasra Rafi
We construct infinite families of closed hyperbolic surfaces that are local maxima for the systole function on their respective moduli spaces. The systole takes values along a line…