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We consider the problem of distortion minimal morphing of ndimensional compact connected oriented smooth manifolds without boundary embedded in R n+1 . Distortion involves bending and stretching. In this paper, minimal distortion is defined (with respect to stretching) 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,doi:10.1216/rmj-2009-39-1-11 fatcat:pcjrlfxrm5fipfrzj36qono5ae