In the published version of the paper:
• Laurent Younes, Peter W. Michor, Jayant Shah, David Mumford: A Metric on Shape Space with Explicit Geodesics. Rend. Lincei Mat. Appl. 9 (2008) 25-57. arXiv:0706.4299.
the following errors have occurred:

On page 3 (page 26/27 in the printed version) in the geodesic equation in the form of $c_{tt}=\dots$ the expression $-\overline{\langle\langle D_s c_t, v\rangle\rangle}$ should be $+\overline{\langle D_s c_t,v\rangle}$.
Similarly in the geodesic equation $u_t = \dots$ some lines further down.

On page 32/33 (page 55 in the printed version) the last minus in equation (23) should be a plus.

On page 33 in Theorem 7.2: "For each $k \ge 3/2$" should be "For each $k \ge 3$".

The version on Peter Michor's homepage has not yet been corrected.