2 problems

Let $M$ be a manifold of dimension at least $3$, and let $\operatorname{Diff}_\mu(M)$ denote its group of volume-preserving diffeomorphisms equipped with the right-invariant $H^s$…

For a group of diffeomorphisms, define the distance threshold by … the smoothness threshold by … and the Fredholm threshold by … Here $d_s$ is the $H^s$ geodesic distance,…