Parametric Geometric Inequalities and Weyl Law for the Volume Spectrum

Explore a seminar on Spectral Geometry that delves into parametric geometric inequalities and the Weyl law for the volume spectrum. Discover how the isoperimetric inequality and coarea inequality, fundamental tools in Geometric Analysis, can be applied to continuous families of submanifolds. Investigate the connection between these parametric versions of classical inequalities and the properties of the volume spectrum, which involves volumes of minimal submanifolds arising from Morse theory on the space of flat cycles. Learn about proofs of these inequalities in low dimensions and their applications to the Weyl law for the volume spectrum in higher codimension. Examine the implications for the existence of minimal surfaces and stationary geodesic nets derived from the Weyl law. Gain insights from joint works with Marques and Neves, Larry Guth, and Bruno Staffa in this 58-minute presentation by Yevgeny Liokumovich at the Centre de recherches mathématiques - CRM.