Deformation Minimal Bending of Compact Manifolds: Case of Simple Closed Curves
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 Φ on the set of diffeomorphisms (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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