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Deformation minimal bending of compact manifolds: case of simple closed curves

Bihun O., Chicone C.

Opuscula Mathematica

2008

Vol. 28, no. 1

19-28

The problem of minimal distortion bending of smooth compact embedded con-nected 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.