DOI: 10.7494/opmath.2008.28.1.19 ISSN: 1232-9274

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

Oksana Bihun, Carmen Chicone
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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 \(\text{Diff}(M,N)\). 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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