Minimal Distortion Bending and Morphing of Compact Manifolds

Abstract

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.

References in corpus (1)

• Deformation Minimal Bending of Compact Manifolds: Case of Simple Closed Curves