Seminar| Institute of Mathematical Sciences
Time: Wednesday, June 12th, 2024 , 14:00-15:00
Location：IMS, RS408
Speaker: Xiaochun Rong, Capital Normal University
Abstract: In Riemannian geometry, a maximal rigidity on an n-manifold M of Ricci curvature bounded below by (n−1)H is a statement that a geometric or a topological quantity of M is bounded above by that of an n-manifold of constant sectional curvature H, and “=” implies that M has constant sectional curvature H. A quantitative maximal rigidity of Ricci curvature bounded below by (n − 1)H is a statement that if a geometric quantity is almost maximal, then M admits a nearby metric of constant sectional curvature H (often additional conditions are required). In this talk, we will survey some recent advances in Metric Riemannian geometry in establishing quantitative maximal rigidities.