Sobolev Metrics on Diffeomorphism Groups and the Derived Geometry of Spaces of Submanifolds

Mario Micheli, Peter W. Michor, David Mumford

Given a finite dimensional manifold $N$, the group ${\mathrm{Diff}}_{\mathcal{S}}(N)$ of diffeomorphism of $N$ which fall suitably rapidly to the identity, acts on the manifold…