# Volumes of minimal hypersurfaces and a new systolic inequality

 Orateur: LIOKUMOVITCH Yevgeny Localisation: King's College de Londres, Royaume-Uni Type: Séminaire de géométrie Site: Hors LAMA , IHP Salle: 314 Date de début: 02/11/2015 - 14:30 Date de fin: 02/11/2015 - 14:30

We will prove an upper bound for the volume of a minimal hypersurface in a closed Riemannian manifold conformally equivalent to a manifold with $\mathrm{Ric}>-(n-1)$. In the second part of the talk we will construct a sweepout of a closed 3-manifold with positive Ricci curvature by $1$-cycles of controlled length and prove a systolic inequality for such manifolds. These are joint works with Parker Glynn-Adey (Toronto) and Xin Zhou (MIT)