Research Project: Several recent results suggest that differential-geometric results, which have been developed for specific infinite-dimensional manifolds of e.g. diffeomorphism  groups or spaces of immersions, can be obtained in a unified way on more general spaces. For example, the perturbative results for Laplace operators of our previous ESI-Research in Team lead to local well-posedness of the geodesic equation not only on spaces of Riemannian metrics but also on many other manifolds of mappings. As a further example, several completeness results for diffeomorphism groups can be obtained by generic arguments on half-Lie groups, as we intend to show in our first goal. The second goal of the project is to further develop and summarize the general theory of infinite-dimensional Riemannian geometry and to present it in a unified way as part of a book project.

Research Team: Martin Bauer (Florida State U), Philipp Harms (NTU Singapore), Peter W. Michor (U Vienna)

Research Stays: May 23 - July 1, 2022