Quantitative Topology and Geometric Inequalities

Explore a 59-minute mathematics lecture delving 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 generate geometric inequalities that connect minimal object sizes to spatial geometric properties including volume, diameter, and curvature.