Infinite-dimensional Geometry 4.5: Geodesic completeness and the Hopf-Rinow theorem
Channel: Alexander Schmeding
Date: 2020-11-14

We discuss various notions of completeness for Riemannian manifolds together with the famous Hopf-Rinow theorem. As we will see for Grossman's ellipsoid, the Hopf-Rinow theorem fails in infinite-dimensions.

This is part of the course MAT331: Topics in Analysis at the University of Bergen in Fall 2020. 
This course (and the lecture) was supported by Trond Mohn foundation within the Pure Mathematics in Norway program (https://www.puremath.no/).