Macroscopic Scalar Curvature and Local Collapsing

Explore the concept of macroscopic scalar curvature and its implications in a one-hour lecture presented by Stéphane Sabourau. Delve into a compelling result concerning Riemannian metrics on closed manifolds with hyperbolic metrics. Discover how the macroscopic scalar curvature, when greater than or equal to that of the hyperbolic metric, leads to a lower bound on volume. Gain insights into the intricate argument involving collapsing techniques and volume localization in metric geometry. Enhance your understanding of advanced topics in differential geometry and topology through this in-depth presentation from the Applied Algebraic Topology Network.