Energy of Knots and Conformal Geometry is popular PDF and ePub book, written by Jun O'Hara in 2003, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Energy of Knots and Conformal Geometry can be Read Online from any device for your convenience.
Energy of Knots and Conformal Geometry Book PDF Summary
Energy of knots is a theory that was introduced to create a OC canonical configurationOCO of a knot OCo 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 OC canonical configurationOCO 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. Contents: In Search of the OC Optimal EmbeddingOCO of a Knot: -Energy Functional E (); On E (2); L p 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 E sin (c) 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 S 3; Conformal Moduli of a Solid Torus; Kirchhoff Elastica; Open Problems and Dreams. Readership: Graduate students and researchers in geometry & topology and numerical & computational mathematics."
Detail Book of Energy of Knots and Conformal Geometry PDF
- Author : Jun O'Hara
- Release : 29 September 2024
- Publisher : World Scientific
- ISBN : 9812795308
- Genre : Mathematics
- Total Page : 308 pages
- Language : English
- PDF File Size : 14,9 Mb
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