Distortion Minimal Morphing: The Theory for Stretching

Oksana Bihun, Carmen Chicone
2009 Rocky Mountain Journal of Mathematics  
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,
more » ... nifolds is given, and the existence of minimal distortion morphs between every pair of isotopic embedded manifolds is proved. MSC 2000 Classification: 58E99
doi:10.1216/rmj-2009-39-1-11 fatcat:pcjrlfxrm5fipfrzj36qono5ae