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Energy of knots and conformal geometry [[electronic resource] /] / Jun O'Hara
| Energy of knots and conformal geometry [[electronic resource] /] / Jun O'Hara |
| Autore | O'Hara Jun |
| Pubbl/distr/stampa | River Edge, NJ, : World Scientific, c2003 |
| Descrizione fisica | 1 online resource (306 p.) |
| Disciplina |
514.224
514/.224 |
| Collana | K & E series on knots and everything |
| Soggetto topico |
Knot theory
Conformal geometry |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-93571-9
9786611935719 981-279-530-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910454278703321 |
O'Hara Jun
|
||
| River Edge, NJ, : World Scientific, c2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Energy of knots and conformal geometry [[electronic resource] /] / Jun O'Hara
| Energy of knots and conformal geometry [[electronic resource] /] / Jun O'Hara |
| Autore | O'Hara Jun |
| Pubbl/distr/stampa | River Edge, NJ, : World Scientific, c2003 |
| Descrizione fisica | 1 online resource (306 p.) |
| Disciplina |
514.224
514/.224 |
| Collana | K & E series on knots and everything |
| Soggetto topico |
Knot theory
Conformal geometry |
| ISBN |
1-281-93571-9
9786611935719 981-279-530-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910782116803321 |
|
O'Hara Jun
|
||
| River Edge, NJ, : World Scientific, c2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Energy of knots and conformal geometry [[electronic resource] /] / Jun O'Hara
| Energy of knots and conformal geometry [[electronic resource] /] / Jun O'Hara |
| Autore | O'Hara Jun |
| Pubbl/distr/stampa | River Edge, NJ, : World Scientific, c2003 |
| Descrizione fisica | 1 online resource (306 p.) |
| Disciplina |
514.224
514/.224 |
| Collana | K & E series on knots and everything |
| Soggetto topico |
Knot theory
Conformal geometry |
| ISBN |
1-281-93571-9
9786611935719 981-279-530-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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 |
| Record Nr. | UNINA-9910820356403321 |
|
O'Hara Jun
|
||
| River Edge, NJ, : World Scientific, c2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||