Title
On the structure of RCD+CBA spaces
Abstract
RCD spaces provide a synthetic framework for lower Ricci curvature bounds on metric measure spaces, while CBA spaces encode a synthetic upper sectional curvature bound via triangle comparison. Kapovitch, Kell and Ketterer showed that a space that simultaneously satisfies these two synthetic curvature bounds is a smooth manifold equipped with a non-smooth Riemannian metric. In this talk, we further explore the geometric and topological structure of RCD+CBA spaces. Under such a mixed curvature bound, we establish the Heintze--Margulis type estimate, volume convergence theorem, uniform injectivity radius bounds, diffeomorphism finiteness theorem and a fibration theorem for collapsing sequences. This is based on the joint work with Ruobing Zhang.
