LEADER 05034nam  2200673Ia 450 
001 9910782116803321
005 20230617040907.0
010   $a1-281-93571-9
010   $a9786611935719
010   $a981-279-530-8
035   $a(CKB)1000000000537839
035   $a(EBL)1679573
035   $a(OCoLC)879023794
035   $a(SSID)ssj0000147322
035   $a(PQKBManifestationID)11146671
035   $a(PQKBTitleCode)TC0000147322
035   $a(PQKBWorkID)10012063
035   $a(PQKB)11166940
035   $a(MiAaPQ)EBC1679573
035   $a(WSP)00005229
035   $a(Au-PeEL)EBL1679573
035   $a(CaPaEBR)ebr10255786
035   $a(CaONFJC)MIL193571
035   $a(EXLCZ)991000000000537839
100   $a20030110d2003      uy             0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aEnergy of knots and conformal geometry$b[electronic resource] /$fJun O'Hara
210   $aRiver Edge, NJ $cWorld Scientific$dc2003
215   $a1 online resource (306 p.)
225 1 $aK & E series on knots and everything ;$vv. 33
300   $aDescription based upon print version of record.
311   $a981-238-316-6 
320   $aIncludes bibliographical references (p. 271-284) and index.
327   $aContents               ; 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
327   $a2.2 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
327   $a3.4 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
327   $a3.9.1 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)
327   $a4.3 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
327   $aChapter 5 Numerical experiments
330   $a Energy of knots is a theory that was introduced to create a "canonical configuration" of a knot - a beautiful knot which represents its knot type. This book introduces several kinds of energies, and studies the problem of whether or not there is a "canonical configuration" of a knot in each knot type. It also considers this problems in the context of conformal geometry. The energies presented in the book are defined geometrically. They measure the complexity of embeddings and have applications to physical knotting and unknotting through numerical experiments. <br><i>Contents:</i><ul><li><i><i
410  0$aK & E series on knots and everything ;$vv. 33.
606   $aKnot theory
606   $aConformal geometry
615  0$aKnot theory.
615  0$aConformal geometry.
676   $a514.224
676   $a514/.224
700   $aO'Hara$b Jun$01477491
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910782116803321
996   $aEnergy of knots and conformal geometry$93692681
997   $aUNINA