Friday, August 2, 2019
08/02/2019 - 10:00am
I will discuss the infimum of the renormalized volume for convex-cocompact hyperbolic manifolds, as well as describing how a sequence converging to such values behaves. In particular, we show that the renormalized volume is continuous under the appropriate notion of limit. This result generalizes previous work in the subject.
08/02/2019 - 1:00pm
Geodesic nets on a Riemannian manifold are critical points of the length functional on embedded graphs connecting a given set of boundary points. We are interested in the connection between the number of boundary points and the possible structures of such nets, in particular how many inner (balanced) vertices a net can have if it has few boundary points. In this talk, we will do three things: We will survey some important questions and conjectures. We will prove that on a non-positively curved Riemannian plane, geodesic nets with three boundary points can have at most one balanced vertex. And we will present curious and geometrically pleasing examples and constructions shedding light on some of the properties and possible structures of geodesic nets.