Uniform convexity in $L^p$ Mabuchi geometry, the space of rays, and geodesic stability
Uniform convexity in $L^p$ Mabuchi geometry, the space of rays, and geodesic stability
The main purpose of this paper is to explore the metric geometry of $L^p$ Mabuchi geodesic rays associated to a Kahler manifold $(X,\omega)$, and to provide applications to stability and existence of canonical metrics. First we show that the $L^p$ Mabuchi metric spaces are uniformly convex for $p >1$, immediately …