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
  • Received: 2007-01-31.
  • Accepted: 2007-06-10.
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Cite this article as:
Oksana Bihun, Carmen Chicone, Deformation minimal bending of compact manifolds: case of simple closed curves, Opuscula Math. 28, no. 1 (2008), 19-28

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