Opuscula Math. 28, no. 1 (2008), 19-28
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.
About the authors ▼
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
About the article ▼
Received: 2007-01-31.
Accepted: 2007-06-10.
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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