Opuscula Mathematica

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

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



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.
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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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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