Deformation Minimal Bending of Compact Manifolds: Case of Simple Closed Curves
Abstract
Description
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 $Φ$ on the set of diffeomorphisms $\diff(M,N)$. We derive the Euler-Lagrange equation for $Φ$ and determine smooth minimizers of $Φ$ in case $M$ and $N$ are simple closed curves.
Typos corrected to match the final version of the paper, which has appeared in Opuscula Mathematica in January, 2008
Typos corrected to match the final version of the paper, which has appeared in Opuscula Mathematica in January, 2008