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

Oksana Bihun·Carmen Chicone
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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 $Φ$ 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.

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Oksana Bihun, Carmen Chicone. 2008-01-23. Deformation Minimal Bending of Compact Manifolds: Case of Simple Closed Curves. https://arxiv.org/abs/math/0701901

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