Volumes of minimal hypersurfaces and stationary geodesic nets

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Yevgeny Liokumovich , Imperial College London
Fine Hall 314

We will prove an upper bound for the volume of a minimal hypersurface in a closed Riemannian manifold conformally equivalent to a manifold with 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 an upper bound for the length of a stationary geodesic net. These are joint works with Parker Glynn-Adey (Toronto) and Xin Zhou (MIT).