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E-raamat: Energy Of Knots And Conformal Geometry

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(Tokyo Metropolitan Univ, Japan)
  • Formaat: 304 pages
  • Sari: Series on Knots & Everything 33
  • Ilmumisaeg: 25-Mar-2003
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789814486408
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Energy Of Knots And Conformal GeometrySuurem pilt
  • Formaat: 304 pages
  • Sari: Series on Knots & Everything 33
  • Ilmumisaeg: 25-Mar-2003
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • Keel: eng
  • ISBN-13: 9789814486408
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Energy of knots is a theory that was introduced to create a "canonical configuration" of a knot - a beautiful knot which represents its knot type. This book introduces several kinds of energies, and studies the problem of whether or not there is a "canonical configuration" of a knot in each knot type. It also considers this problem in the context of conformal geometry. The energies presented in the book are defined geometrically. They measure the complexity of embeddings and have applications to physical knotting and unknotting thorough numerical experiments.

O'Hara (mathematics, Tokyo Metropolitan University introduces several kinds of energies of knots, studies the problem of whether there is a canonical configuration of a knot in each knot type, and considers this problem in the context of conformal geometry. The energies presented are defined geometrically and measure the complexity of embeddings. They have applications to various fields of natural science. Annotation (c) Book News, Inc., Portland, OR (booknews.com)
In Search of the "Optimal Embedding" of a Knot: -Energy Functional E(
); On E(2); Lp Norm Energy with Higher Index; Numerical Experiments; Stereo
Pictures of E(2) Minimizers; Energy of Knots in a Riemannian Manifold;
Physical Knot Energies; Energy of Knots from a Conformal Geometric Viewpoint:
Preparation from Conformal Geometry; The Space of Non-Trivial Spheres of a
Knot; The Infinitesimal Cross Ratio; The Conformal Sin Energy Esin ; Measure
of Non-Trivial Spheres; Appendices: Generalization of the Gauss Formula for
the Linking Number; The 3-Tuple Map to the Set of Circles in S3; Conformal
Moduli of a Solid Torus; Kirchhoff Elastica; Open Problems and Dreams.
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Püsilink: https://www.kriso.ee/db/97898144864082e.html