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Авторизация |
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Поиск по указателям |
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O`Hara J. — Energy of knots and conformal geometry |
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Предметный указатель |
244
-energy 20 28
-energy polynomial 79
124
249
58
124
-self avoiding voltage 10
see “Energy”
255
-modified -off diagonal electrostatic energy 15
-modified -self avoiding voltage 15
-modified electrostatic energy 22
see “Voltage”
40 41
136
39
180
184
4-tuple map, extended 186
4-tuple map, of 148
4-tuple map, of a knot 178
Absolute circular self-linking number a la Gauss 254
Admissible polygonal knot 75
Admissible solid torus 75
Annulus, cross-separating annulus 158
Annulus, Lorentzian modulus of 156
Annulus, maximal cross-separating annulus 158
Annulus, maximal non-trivial 232
Annulus, maximal non-trivial, for links 241
Annulus, modulus of 156
Annulus, non-trivial 232
Annulus, non-trivial, for links 241
Area of the twice tangent spheres 223
Argument of the infinitesimal cross ratio 204
Asymptotic crossing number 261
Atwt(K) 223
Average crossing number 249
Base, circls 177 180 183 184
Base, sphere (circle, or points) 152
BASIC 7
Beads radius 131
beta function 79
Brylinski's beta function see “Beta function”
Canonical symplectic form of a cotangent bundle 191
Captured by a polygonal knot 75
Center of a pencil 152
Charge 5
Circular Gauss map 253
Combined angle 60
Complete family of N,r-polygonal knots 76
Complete system of solid tori 75
Concircular, set of (2,2)-points 180
Concircular, set of generalized, points 186
Concircular, set of osculating, points 184
Concircular, set of, points in 147
Concircular, set of, points of a knot 177
Configuration space 147
Conformal, energy 40 208
Conformal, -energy 59
Conformal, energy 213
Conformal, energy 61
Conformal, angle 41 204
Conformal, angle 39
Conformal, diffeomorphism 138
Conformal, group 136
Conformal, modulus of a solid torus 260
Conformal, sin X-energy 59
Conformal, transformation 35 136
Conformal, transportation 41
Conformal, unit — transportation 40 173
Conformally transported unit vector 173
Conformally transported, unit vector 40
Conformally transported, vector 41
Cosine formula 39
Counter term see “Knot energy functional”
Cross ratio of four ordered points 149
Cross-separating, annulus 158
Cross-separating, sphere 158
Cross-strand 232
Curvature see “Geodesic curvature”
De Sitter space 137
Distortion 28
Doubly critical self distance, essential 131
Elastica 263
Energy minimizer 6
Energy, -energy functional 67
Energy, -energy 20 28
Energy, -energy polynomial 79
Energy, -diagonal electrostatic energy 11
Energy, 12
Energy, 28
Energy, 29 35 204
Energy, 20
Energy, 15
Energy, 64
Energy, 46
Energy, 225
Energy, 213
Energy, 61
Energy, -modified -off diagonal electrostatic energy 15
Energy, -modified electrostatic energy 22
Energy, beta function 79
Energy, conformal energy 208
Energy, conformal energy 213
Energy, Eapm 101
Energy, imaginary cross ratio energy 213
Energy, Moebius energy 29
Energy, mutual conformal energy 209
Energy, mutual conformal energy 222
Energy, renormalization of electrostatic energy 12
Energy, scale invariant energy 114
Energy, unit density -energy 101
Energy, unit quantity energy 114
Energy, X-energy 59
ess.dcsd(h) 131
| ess.sd(h) 131
Essential doubly critical self distance 131
Essential self distance 131
Finiteness of knot types 7
Gauss, absolute circular self-linking number a la Gauss 254
Gauss, circular Gauss map 253
Gauss, linking number formula 243
Geodesic curvature 154
GI(f,g) 244
Global radius of curvature, at a point 121
Global radius of curvature, minimum 124
Gromov's distortion see “Distortion”
Ideal knot 118
Imaginary cross ratio energy 213
INDEX 20 64 101
Infinitesimal cross ratio, argument of 204
Infinitesimal cross ratio, of a knot 203
Infinitesimal cross ratio, of the complex plane 189
Inflation radius 118
Intersecting (two spheres) 154
Inversion in a sphere 34
Inverted open knot 37
Knot energy functional, counter term 13 19 20
Knot energy functional, principal term 20
Knot energy functional, with respect to the -topology 5
L-orthogonal 136
Light-cone 136
Light-like 136
Linking number, absolute circular self-linking number a la Gauss 254
Linking number, Gauss formula 243
Linking number, GI(f,g) 244
Linking number, self-linking number 246
Lorentz group 111 136
Lorentzian, exterior product 143
Lorentzian, modulus of an annulus 156
Lorentzian, modulus of four points 158
Lorentzian, pseudo inner product 110 135
Lorentzian, quadratic form 135
Maximal, cross-separating annulus 158
Maximal, non-trivial annulus 232
Maximal, non-trivial annulus for links 241
Measure of non-trivial spheres 225
Minimum distance 128
Minkowski space 136
Modulus, conformal, of a solid torus see “Conformal modulus”
Modulus, Lorentzian see “Lorentzian”
Modulus, of a knot 232
Modulus, of a link 241
Modulus, of an annulus 156
Modulus, of four ordered points 158
Moebius, energy 29
Moebius, group 138
Moebius, transformation 34 138
Mutual, conformal energy 209
Mutual, conformal energy 222
Nested (two spheres) 154
Non-trivial, annulus 232
Non-trivial, annulus for links 241
Non-trivial, sphere 175
Non-trivial, sphere in the strict sense 175
Normal projection energy symmetric 60
Optimal embedding 7
Osculating, circle 119
Osculating, sphere 119
Osculating, sphere map 186
Pencil, base sphere (circle, or points) of 152
Pencil, center of 152
Pencil, Poncelet 152
Poncelet, pencil 152
Poncelet, points 153
Principal part see “Knot energy functional”
Pull-tight 7
Renormalization, electrostatic energy 12
Renormalization, of -modified electrostatic energy 20
Renormalization, of -modified voltage 19
Residue formula 57
Rl(K) 118
Ropelength 118
Scale invariant energy 114
Self, self-repulsive 5
Self, essential self-distance 131
Self, linking number 246
Set of concircular points see “Concircular”
Sl(f) 246
Space-like 136
Sphere, area of the twice tangent spheres 223
Sphere, cross-separating sphere 158
Sphere, inversion in a sphere 34
Sphere, measure of non-trivial spheres 225
Sphere, non-trivial sphere 175
Sphere, non-trivial sphere in the strict sense 175
Sphere, osculating 119
Sphere, twice tangent 173
Sphere, twice tangent sphere 119
Sphere, twice tangent, of a knot 179
Strand, cross-strand 232
Strand, minimal cross-strand 232
Symmetric normal projection energy 60
Thickness 117
Thk(K) 118
Tight 7
Time-like 136
Total variation of the conformally transported unit tangent vectors 255
transportation see “(unit) conformal transportation”
Twice tangent sphere 119
Twice tangent sphere map 181
Twice tangent sphere, of a knot 179
Unit, density -energy 101
Unit, quantity energy 114
Voltage, -self avoiding voltage 10
Voltage, -modified -self avoiding voltage 15
Voltage, 19
Voltage, 15
Wasted length of an inverted open knot 39
Wr(f) 246
Writhe 246
Writhe, direction 246
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