  We consider the problem of distortion minimal morphing of $n$-dimensional
compact connected oriented smooth manifolds without boundary embedded in
$\R^{n+1}$. Distortion involves bending and stretching. In this paper, minimal
distortion (with respect to stretching) is defined as the infinitesimal
relative change in volume. The existence of minimal distortion diffeomorphisms
between diffeomorphic manifolds is proved. A definition of minimal distortion
morphing between two isotopic manifolds is given, and the existence of minimal
distortion morphs between every pair of isotopic embedded manifolds is proved.
