Distortion Minimal Morphing I: The Theory For Stretching
Differential Geometry
2010-11-17 v2 Optimization and Control
Abstract
We consider the problem of distortion minimal morphing of -dimensional compact connected oriented smooth manifolds without boundary embedded in . 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.
Cite
@article{arxiv.math/0605668,
title = {Distortion Minimal Morphing I: The Theory For Stretching},
author = {Oksana Bihun and Carmen Chicone},
journal= {arXiv preprint arXiv:math/0605668},
year = {2010}
}