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Energy Of Knots And Conformal Geometry - Jun O'Hara

Energy Of Knots And Conformal Geometry

(Autor)

Buch | Hardcover
304 Seiten
2003
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-238-316-7 (ISBN)
CHF 149,95 inkl. MwSt
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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 whether or not there is a "canonical configuration" of a knot in each knot type.
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 problems 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 through numerical experiments.

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.

Erscheint lt. Verlag 26.3.2003
Reihe/Serie Series on Knots & Everything ; 33
Verlagsort Singapore
Sprache englisch
Themenwelt Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 981-238-316-6 / 9812383166
ISBN-13 978-981-238-316-7 / 9789812383167
Zustand Neuware
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