Distortion Minimal Morphing I: The Theory For Stretching

Details Distortion Minimal Morphing I: The Theory For Stretching Distortion Minimal Morphing I: The Theory For Stretching

2006-05-25

arxiv.org/abs/math/0605668v2

Rocky Mountain Journal of Mathematics, Vol. 39, No. 1 (2009) 11--26

Mathematics

Differential Geometry

Scientific paper

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.

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