Möbius energy of knots and unknots (Q1319109)
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scientific article; zbMATH DE number 549321
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Möbius energy of knots and unknots |
scientific article; zbMATH DE number 549321 |
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Möbius energy of knots and unknots (English)
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12 April 1994
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The authors prove: -- the Möbius invariance of the energy of a simple closed curve in \(\mathbb{R}^ 3\) and that the energy bounds the average crossing number of curves in \(\mathbb{R}^ 3\); -- the existence of curves which minimize the energy in the family of loops representing any given irreducible knot; -- curves of finite energy are topologically tame and -- variational formulas for the gradient of the energy.
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Möbius invariance
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energy of a simple closed curve in \(\mathbb{R}^ 3\)
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average crossing number
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curves which minimize the energy
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topologically tame
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gradient of the energy
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