4 papers
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…
A recursion for the volume of the moduli space of hyperbolic spheres
Michele Ancona, Damien Gayet
We prove the existence of a non-linear recursive relation for the volume of the moduli space of hyperbolic spheres with conical points or geodesic boundaries. This relation general…
Lower bound for the Cheeger constant of random complex curves
Michele Ancona, Damien Gayet
In this paper, we provide a lower bound for the Cheeger constant and the spectral gap for random complex curves in $\C P^2$. The complex curve is endowed with the restriction of th…
On the curvatures of random complex submanifolds
Michele Ancona, Damien Gayet
For any integers and satisfying , we show that the expected volume fraction of a random degree complex submanifold of $\C\mathbb{P}^n$…