Analyticity of Riemannian exponential maps on ${\rm Diff}(\T)$
  We study the exponential maps induced by Sobolev type right-invariant (weak) Riemannian metrics of order $k\ge1$ on the Lie group of smooth, orientation preserving diffeomorphisms of the circle. We prove that each of them defines an {\em analytic} Fr\'echet chart of the identity. 
T. Kappeler, E. Loubet, P. Topalov