Recent progress on geometric analysis and Riemannian geometry: Scalar curvature and the length of a shortest closed geodesic
Presenter
October 21, 2024
Keywords:
- mean curvature flow
- Ricci flow
- fully nonlinear flows
- general relativity
- mass
- Ricci curvature
- scalar curvature
- sectional curvature
- symmetry
- Riemannian geometry
- groups actions
- minimal surfaces
- stability
MSC:
- 35-XX - Partial differential equations
- 49-XX - Calculus of variations and optimal control
- optimization
- 53-XX - Differential geometry
- 58-XX - Global analysis
- analysis on manifolds
- 83-XX - Relativity and gravitational theory
Abstract
Let M be a closed Riemannian 3-manifold with scalar curvature bounded below by some positive constant k. We will prove that there exists a closed non-trivial geodesic on M of length at most $\frac{c}{\sqrt{k}}$. (Joint with Y. Liokumovich, D. Maximo.)