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

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

2007-01-31

arxiv.org/abs/math/0701901v2

Opuscula Mathematica, Vol. 28, No. 1 (2008) 19-28

Mathematics

Optimization and Control

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

Scientific paper

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.

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