# Henrik Matthiesen, MPI Bonn: "The systole of large genus minimal surfaces in positive Ricci curvature"

Jul 12, 2018 from 04:15 PM to 05:45 PM

Abstract:

There are many results on the space of minimal surfaces of bounded genus or index in ambient three manifolds having some positivity condition on the curvature, e.g. positive Ricci or scalar curvature. In contrast, there are only few results describing asymptotic properties of a sequence of minimal surfaces with unbounded genus. We show that for such a sequence the systole, i.e. the length of a shortest non-contractible curve, has to tend to zero, if the ambient manifold has positive Ricci curvature. This is joint work with Anna Siffert.