Joint Geometry and Analysis seminar: Volume of closed Riemannian manifolds and geometric invariants related to their area-minimising hypersurfaces

Dr Lucas Ambrozio (University of Warwick) will present his research in Analysis and Geometry.

Several variational methods used to find minimal submanifolds in a closed Riemannian manifold define critical levels of the area functional, and it is interesting to understand how much information these numbers contain about the ambient geometry itself. This can be done by comparison to other geometric invariants, for example, curvature and volume. In this talk, we will focus on the space of unit volume metrics, mainly when the underlying manifolds are real projective spaces and the minimal submanifolds corresponding to the critical levels are of minimising type. This is joint work with Rafael Montezuma.