Discrete Möbius energy (Q2930075)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Discrete Möbius energy |
scientific article |
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Discrete Möbius energy (English)
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17 November 2014
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Möbius energy
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polygonal knot
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minimizers
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discrete energy
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knot energy
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\(\Gamma\)-convergence
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This paper deals with a discrete version of the Möbius energy defined on equilateral polygons with \(n\) segments. The author proves the Möbius energy convergence results for the polygonal approximations of a smooth knot (if the limit of the discrete approximations belongs to the same knot class). The author also shows that the unique minimizer amongst all polygons is the regular \(n\)-gon, and hence that discrete overall minimizers converge to the round circle.
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