Abstract:
The optimal path to circumnavigate the earth is to follow a closed geodesic. For nonround surfaces, the length of such closed geodesics may be arbitrarily small. We show that infinitesimally short geodesics produce a quantifiable amount of curvature of the surface, measured in terms of the Willmore energy. This is joint work with M. Müller (Freiburg) and C. Scharrer (Bonn).