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Energy of knots and conformal geometry [[electronic resource] /] / Jun O'Hara



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Autore: O'Hara Jun Visualizza persona
Titolo: Energy of knots and conformal geometry [[electronic resource] /] / Jun O'Hara Visualizza cluster
Pubblicazione: River Edge, NJ, : World Scientific, c2003
Descrizione fisica: 1 online resource (306 p.)
Disciplina: 514.224
514/.224
Soggetto topico: Knot theory
Conformal geometry
Soggetto genere / forma: Electronic books.
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references (p. 271-284) and index.
Nota di contenuto: Contents ; Preface ; Part 1 In search of the ""optimal embedding"" of a knot ; Chapter 1 Introduction ; 1.1 Motivational problem ; 1.2 Notations and remarks ; Chapter 2 a-energy functional E(a) ; 2.1 Renormalizations of electrostatic energy of charged knots
2.2 Renormalizations of r-a-modified electrostatic energy Ea 2.3 Asymptotic behavior of r-a energy of polygonal knots ; 2.4 The self-repulsiveness of E( a ) ; Chapter 3 On E(2) ; 3.1 Continuity ; 3.2 Behavior of E(2) under ""pull-tight"" ; 3.3 Mobius invariance
3.4 The cosine formula for E(2) 3.5 Existence of E(2) minimizers ; 3.6 Average crossing number and finiteness of knot types ; 3.7 Gradient regularity of E(2) minimizers and criterion of criticality ; 3.8 Unstable E(2)-critical torus knots ; 3.9 Energy associated to a diagram
3.9.1 General framework 3.9.2 ""X-energy"" ; 3.10 Normal projection energies ; 3.11 Generalization to higher dimensions ; Chapter 4 Lp norm energy with higher index ; 4.1 Definition of (a p)-energy functional for knots eap ; 4.2 Control of knots by Eap (eap)
4.3 Complete system of admissible solid tori and finiteness of knot types 4.4 Existence of Eap minimizers ; 4.5 The circles minimize Eap ; 4.6 Definition of a-energy polynomial for knots ; 4.7 Brylinski's beta function for knots ; 4.8 Other Lp-norm energies
Chapter 5 Numerical experiments
Sommario/riassunto: 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. <br><i>Contents:</i><ul><li><i><i
Titolo autorizzato: Energy of knots and conformal geometry  Visualizza cluster
ISBN: 1-281-93571-9
9786611935719
981-279-530-8
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910454278703321
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Serie: K & E series on knots and everything ; ; v. 33.