Opuscula Math. 28, no. 1 (2008), 19-28

Opuscula Mathematica

# 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 $$\Phi$$ 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.

Keywords: minimal deformation, distortion minimal, geometric optimization.

Mathematics Subject Classification: 58E99.

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• Oksana Bihun
• University of Missouri-Columbia, Department of Mathematics, Columbia, Missouri 65211, USA
• Carmen Chicone
• University of Missouri-Columbia, Department of Mathematics, Columbia, Missouri 65211, USA