Differential Geometry Seminar
Riemannian manifolds with no conjugate points or no focal points are natural generalizations of those with nonpositive sectional curvature. However, they are defined using synthetic conditions about geodesics rather than strict curvature bounds. This talk will begin with an overview of curvature comparison in Riemannian geometry. We will then discuss the extent to which classical theorems in Riemannian geometry and geometric analysis about nonpositively curved spaces generalize to those with no conjugate points, along with applications to other questions in Riemannian geometry.