Abstract: I will talk about parametric versions of two classical inequalities in geometry: the isoperimetric inequality and coarea inequality. These two inequalities are basic tools in analyzing properties of submanifolds in Riemannian geometry. The parametric versions are statements about a family of submanifolds as opposed to one single submanifold. I will discuss proofs of some parametric inequalities in low dimensions, the higher dimensional versions that are still open and their applications to minimal surfaces and stationary geodesic nets. The talk will be based on joint works with Larry Guth and Bruno Staffa.
Speaker: Yevgeny Liokumovich is currently an assistant professor at University of Toronto. He obtained his Ph.D. at University of Toronto in 2015 under the supervision of Alexander Nabutovsky and Regina Rotman. His interests lie at the intersection of Geometric Analysis, Quantitative Topology and Geometric Measure Theory. He is also interested in problems in 3-manifold topology.
ID: 811 0028 7715
Passcode: 165951
