Quantitative Topology and Geometric Inequalities

Explore a 56-minute mathematics lecture that delves into quantitative versions of existence theorems in Geometric Calculus of Variations, originally proven through Algebraic Topology methods. Learn about A. Fet and L. Lyusternik's theorem on periodic geodesics in closed Riemannian manifolds, J. P. Serre's theorem on infinite geodesics between point pairs, and X. Zhou's recent findings on geodesic chords in complete manifolds. Discover how these quantitative interpretations lead to geometric inequalities that connect minimal object sizes with spatial geometric properties including volume, diameter, and curvature.