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