Minimal Distortion Bending and Morphing of Compact Manifolds

Details Minimal Distortion Bending and Morphing of Compact Manifolds Minimal Distortion Bending and Morphing of Compact Manifolds

2007-08-30

arxiv.org/abs/0708.4235v1

Mathematics

Optimization and Control

Scientific paper

Let $M$ and $N$ be compact smooth oriented Riemannian $n$-manifolds without boundary embedded in $\mathbb{R}^{n+1}$. Several problems about minimal distortion bending and morphing of $M$ to $N$ are posed. Cost functionals that measure distortion due to stretching or bending produced by a diffeomorphism $h:M \to N$ are defined, and new results on the existence of minima of these cost functionals are presented. In addition, the definition of a morph between two manifolds $M$ and $N$ is given, and the theory of minimal distortion morphing of compact manifolds is reviewed.

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