## Right-invariant Sobolev metrics ${H}^{s}$ on the diffeomorphisms group of the circle    [PDF]

Joachim Escher, Boris Kolev
We study the geodesic flow on the diffeomorphisms group of the circle with
respect to the right-invariant metric induced by the fractional Sobolev norm
$H^s$ for $s\ge1/2$. We show that the corresponding initial value problem
possesses a maximal solution in the smooth category and that the Riemannian
exponential mapping is a smooth diffeomorphism from a neighbourhood of 0 in
$C^{\infty}(S)$ onto a neighbourhood of the identity in $Diff^{\infty}(S)$.
View original: http://arxiv.org/abs/1202.5122