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

Oksana Bihun; Carmen Chicone

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

Optimization and Control 2008-01-23 v2 Differential Geometry

Authors: Oksana Bihun , Carmen Chicone

Abstract

The problem of minimal distortion bending of smooth compact embedded connected Riemannian $n$ -manifolds $M$ and $N$ without boundary is made precise by defining a deformation energy functional $\Phi$ on the set of diffeomorphisms $\diff(M,N)$ . We derive the Euler-Lagrange equation for $\Phi$ and determine smooth minimizers of $\Phi$ in case $M$ and $N$ are simple closed curves.

Keywords

minimal distortion bending compact manifolds deformation energy euler-lagrange equation simple closed curves

Cite

@article{arxiv.math/0701901,
  title  = {Deformation Minimal Bending of Compact Manifolds: Case of Simple Closed Curves},
  author = {Oksana Bihun and Carmen Chicone},
  journal= {arXiv preprint arXiv:math/0701901},
  year   = {2008}
}

Comments

Typos corrected to match the final version of the paper, which has appeared in Opuscula Mathematica in January, 2008

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

Abstract

Keywords

Cite

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