1 - Proofs of convergences of the dynamical time warping algorithm when the discretization of the shapes gets finer. In fact this is a tutorial we wrote for our team, about dynamical time warping for shape matching, convergence proofs, and transport on manifold. We anonymized the tutorial for the Nordia submission. We do not expect the reviewer to read this tutorial; however we thought that the reviewer may find interesting some parts described in it. In particular, the frame-boxes on pages 17 and 23 are summaries of the convergence study. convergence_proofs.pdf 2 - Proof of proposition 2 (section 4.1). proof_kernel_KL.pdf