Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Manh Tien Nguyen
I will explain how each function whose Hessian is a multiple of the metric of a Riemannian manifold $M$ corresponds to a monotonicity theorem for minimal surfaces in $M$. When $M$ is the hyperbolic space, such functions arise as the Minkowskian coordinates in the hyperboloid model and they pose constraints on where a minimal surface can pass by in terms of its boundary curve. Using these constraints, one can detect the linkedness of a link in S^3 by counting the number of minimal surfaces in H^4 filling it. If time allows, I will present two different upper bounds of the Graham--Witten's renormalised area obtained from the monotonicity theorems, one by the time coordinate and one by the space coordinate.