The Willmore Functional and Mobius Strips
نویسنده
چکیده
Given a Mobius strip M isometric to a xed rectangle R, characterize the f lat (Gauss curvature K = 0) immersion :M ! R which minimizes W. The physical analog for this problem is to characterize the half-twisted coil of paper (Mobius strip) which has least bending energy. This problem di ers from the classical Willmore problem in three respects: (i) M has a boundary, (ii) M is non-orientable, and (iii) M should be f lat. There are actually two parts to this problem. One is the existence and regularity of a minimizer which is the main subject of this note.
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