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| Lawrynowicz J., Krzyz J. — Quasiconformal Mappings in the Plane: Parametncal Methods |
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| Предметный указатель |
Absolute continuity on lines 6
ACL 2 6
Agard, S. and Gehring, F.W. 51[1]
Ahlfors, L.V. III[5] IV[2 5] 5[5] 12[5] 14[5] 34[5] 37 48 49[1 7] 50[2 52[2 5] 54[5] 84[3] 91[3] 117[5 8] 118[6] 125 135[2] 150[2] 152[2]
Ahlfors, L.V. and Bers, L. IV[1] 37[1] 48[1] 54[1] 125[1] 135[1]
Ahlfors, L.V. and Beurling, A. 50[1 2]
Ahlfors, L.V. and Weill, G. 117[1]
Analyticity of a functional 128 129
angle 52
Arc, boundary 49
Arc, Jordan 1
Arc, locally rectifiable 50
Arzela., C. 42
Ascoli, G. 42
Banach, S. 57 63
Baumgarten, H. 117
Becker, J. 117[1—6]
Becker, J. and Pommerenke, C. 117[1]
Behnke, H. and Sommer, F. 2[1] 47[1]
Belinskii, P.P. IV[1 38 52[1] 135[1 2] 136[1] 138[1] 139[2]
Belinskii, P.P. and Pesin, I.N. 38[1]
Beltrami, E. 12[1] 31 37 98 117 118
Bers, L. IV 12[1] 37 38 48[1 3] 54 125 135[4] 150[2] 155[5]
Bers, L. and Nirenberg, L. 38[1]
Beurling, A. 50
Biluta, P.A. 139
Blaar, H. 117
Bojarski, B. III[2] 12[1 2] 33[1 2] 34 38[1 2] 45[2] 109 117 118
Bojarski, B. and Iwaniec, T. 45[1]
Borel, E. 7—9 50
Calderon, A.P. and Zygmund, A. III[2] 16[2] 24[1 2 3] 31[2] 109[2] 146
Capacity 159 160
Caratheodory, C. 38 46[1] 69[2] 71 78 80 82
Cauchy, A. 57 60 120
Chain rule for the distributional derivatives 37
Characterizations of qc or Q-qc mappings: analytic 5 48—49
Characterizations of qc or Q-qc mappings: analytic geometric 50—51
Characterizations of qc or Q-qc mappings: analytic metric 51—52
Characterizations of qc or Q-qc mappings: analytic without specifying Q 52
Cheng Bao-long 52[1] 135[1]
Coddington, E.A. and Levinson, N. 69[1]
Coefficient of electric conductivity 160
Collingwood, E.F. and Lohwater, A.J. 46[1]
Condenser 159
Condenser plates 159
Condition, orthogonality 81
Continuation of a Q-qc homeomorphism to the boundary 44
Continuity of a functional 127
Convergence, almost uniform 2
Courant, R. IV[1] 46[2] 47[2]
Curve, Jordan 1
Curve, locally rectifiable 50
Delimiting lasers 162
Derivative, Gateaux, of a functional 135
Derivatives, directional 4
Derivatives, distributional LP- 8
Dielectric displacement 160
Dielectric displacement polarization 160
Diffeomorphism 4
Diffeomorphism, quasiconformal 4
Differential, quadratic IV 149 150
Dilatation of the diffeomorphism at a point 4
Dilatation,  144
Dilatation, circular 51
Dilatation, complex 12
Dilatation, maximal, of a Q-qc mapping 4—5
Distance, hyperbolic 50 51
Distortion of cilcular neighbourhoods and angles under Q-qc mappings 51
Distortion of hyperbolic area under Q-qc mappings 116
Distortion, area, under Q-qc mappings 109—116
Distortion, line(ar), under Q-qc mappings 94—108
Dittmar, B. 38[1] 117
Domain, canonical 46
Domain, canonical circular 46
Domain, canonical on a Riemann surface 151
Domain, circular 46
Domain, fundamental 151
Domain, Jordan 1
Domain, parallel slit 47
Duren, P.L. and Lehto, O. 117[1]
Egoroff, D.P. 9
Electric conductivity 160
Electric current-density 157 160
Electric induction 157
Electric permeability 156 157 160
Electric permeability, relative 157
Electric susceptibility 160
Electric susceptibility, entire 160
Equation, differential, Beltrami 12
Equation, integral, Tricomi 31
Equation, parametrical 63 73 81 86 99
Equations of motion for charged particles 156
Equations, Maxwell 157
Equimeasurable functions 109
Extension see Continuation and Mapping conformal with
Extremal length 50
Fait, Maria, Krzyz, J. and Jadwiga Zygmunt 117[1]
Fan Le-le 115 116
Form, normal, of Klein 151
Formula, Green's 8
Fubini, G. 7 12
Function absolutely continuous on lines 6
Function locally LP 7
Function multiplicatively convex 18
Function of forces 157 160
Function, Borel 8
Function, comparison 135
Function, convex 18
Functional, analytic 128 129
Functional, continuous 127
Functional, differentiable in the sense of Gateaux 135
Functions, equimeasurable 109
Gaeteaux, R. 135 141 147—149
Gauss, C.F. III[1] 34[1]
Gehring, F.W. IV 5[2] 8 34[5] 48 49[2] 50 51[1] 52[2] 53 54[3] 109 116[4]
Gehring, F.W. and Lehto, O. 5[1] 8[1] 48[1]
Gehring, F.W. and Reich, E. IV[1] 53[1] 54[1] 109[1]
Gehring, F.W. and vaeisaeiae, J. 50[1] 51[1]
Genus of a surface 151
Goektuerk, Zerrin 117[1] 131[1] 134[1]
Gol'dstein, V.M. 34[1] 109[1]
Golusin, G.M. III[1] IV[2] 48[2]
Goursat, E. 36[1] 69[1] 144[1]
Graves, L.M. 6[1]
Green, G. 8 13—16 26 27 29 35 58 83 161
Groetzsch H. III 4[1] 149[1 2] 150[1]
Group, Fuchsian 152
Group, Fuchsian, of a Riemann surface 152
Group, fundamental 151 162
Grunsky, H. 133
Gutljanskii, V. Ja. 155[1—3]
Gutljanskii, V. Ja. and Scepetev, V.A. 155[1—2]
Hadamard, J. IV[1]
Hahn, O. 150
Hamilton, R.S. 85[1] 154[1]
Harrington, A.N. 160[1]
Hersch, J. 51[1]
Hersch, J. and Pfluger, A. 51[1] 106[1]
Hilbert, D. III 119
Hoelder, O. 12 17—23 30 33 40—42 58—60 138
Homeomorphism, Q-qc 5 48
Homeomorphism, Q-qc, of the closure of a domain bounded by disjoint Jordan curves 5
Homeomorphism, sense-preserving 3
Homotopy of topological mappings III 53 152
Hoy, E. 117
Huebner, O. 106[1]
Identity of the Fuchsian groups of Riemann surfaces 152
Inequality of Calderon — Zygmund 24
Inequality of Grunsky 133
Intensity of electric current 160
| Intensity of the electric field 156
Intensity of the magnetic field 157
interval 1
Iwaniec, T. IV 45
Jacobian 4
Jordan, C. 1 3—5 13 36 38 46 49—52 123 124 144 148 158 159 161 162
Julia, G. IV[1]
Kelingos, J. 51[1] 109[2] 116[2]
Klein, F. 151
Koebe, P. 107 134 151
Komatu, Y. III[1]
Kronecker, L. 95
Kruskal, S.L. IV[1—8] 53[1] 117[6] 135[5 8] 136[4 7] 139[7 8] 150[3 8] 154[4]
Krzyz, J. 50[2] 52 102[1] 117[3 4] 136 155[1]
Krzyz, J. and Lawrynowicz, J. 52[1]
Krzyz, J. and Soni, A.K. 117[1]
Kuehnau, R. IV[1—15] 94[9] 117[1-13] 133[2 3 5] 134[2 10] 155[1—13] 157 160
Kuehnau, R. and Baumgarten, H. 117[1]
Kuehnau, R. and Blaar, H. 117[1]
Kuehnau, R. and Dittmar, B. 117[1]
Kuehnau, R. and Hoy, E. 117[1]
Kuehnau, R. and Niske, W. 117[1]
Kuehnau, R. and Thuring, B. 117[1]
Kuehnau, R. and Timmel, J. 117[1]
Laurent, P. 122 128
Lavrentieff, M.A. III[2] 4[1] 34[2] 51[1 2]
Lawrynowicz, J. IV 45[1] 46[1] 52[3] 53[1 2] 54[5] 67[1 5] 73[5] 80[6 8] 85[7 8] 88[1] 94[4] 98[4] 101[6] 104[4] 106[3] 139[9] 140[4] 160
Layers, delimiting 162
Lebesgue, H. 1 18 69
Lehto, O. III IV[3—6] 4 5 8 12[2] 15 25 34[1] 40 48 102 106 108 117[3—8] 118[4 7] 123 124[7] 125[6 7] 126[7] 127 128[4 6] 130—132 145[6] 155
Lehto, O. and Tammi, O. 117[1]
Lehto, O. and Virtanen, K.I. III[1 2] 4[1 2] 5[1] 21 12[1 2] 15[1 2] 25[1 2] 35[1 2] 2] 102[1 2] 126[1 2] 127[1 2] 155[1 2]
Length, extremal 50
Levinson, N. 69
Lichtenstein, L. III[1] 34[1]
Lines of force 158 160
Lines, equipotential 158
Liouville, J. 42
Loewner, K. III[1]
Lohwater, A.J. 46
Magnetic induction 156 160
Magnetic induction, entire 160
Magnetic permeability 156 160
Magnetic shells 162
magnetic susceptibility 160
Magnetic susceptibility, entire 160
magnetization 160
Mapping, conformal, of the closure of a domain bounded by disjoint Jordan curves 5
Mapping, conformal, with a qc extension 116—134
Mapping, differentiable 4
Mapping, differentiable at a point 3—4
Mapping, open 8
Mapping, Q-qc 4
Mapping, Q-qc, regular 4
Mapping, Q-quasiconformal 4—5
Mapping, qc, close to the identity mapping 52 57—62 104—106
Mapping, qc, extremal IV 150
Mapping, qc, regular 4
Mapping, qc, Teichmuller 80 85
Mapping, qc, with invariant boundary points 80—81 85 86 155
Mapping, qc, with prescribed boundary values 85 153
Mapping, quasiconformal III—IV 5
Mapping, regular 4
Mapping, regular at a point 4
Mapping, Teichmueller 80 85 101
Mapping, Teichmueller, of a disc 80
Mapping, Teichmueller, of a disc, normalized 80
Mapping, Teichmueller, of an annulus, normalized 85
Matrix, Grunsky 133
Maxwell, J.C. 157 161 162
Measure, harmonic 50 51
Measure, inner, of an angle 52
Method of extremal length 50
Method, parametrical, for conformal mappings III IV 116—134
Method, parametrical, for qc mappings III—IV 53—134
Method, variational, for conformal mappings IV
Method, variational, for qc mappings IV 135—155
Method, variational, for qc mappings, Belinskii's 135—144
Method, variational, for qc mappings, Schiffer's 144—150
Minkowski, H. 20 34 56 59 137
Modulus of a doubly connected domain 49—50
Modulus of a family of Jordan arcs or curves 50
Modulus of a quadrilateral 49—50
Momentum 156
Mori, A. 5[1] 48[1] 104[1] 106
Morrey, C.B., Jr. III[1] 2[2] 38[1]
Newman, M.H.A. 3[1] 4
Nirenberg, L. 38
Niske, W. 117
Norm, convex 18
Norm, multiplicatively convex 18
Normalization, hydrodynamic 126
Normalized Teichmueller mapping of a disc 80
Normalized Teichmueller mapping of an annulus 85
Ohm, G. 160
Osgood, W.F. 38 69 78 80 82
Parametrization III-IV 53—134
Parter, S.V. 45[1] 158[1]
Peano, G. 69 78
Pesin, I.N. 38 51[1]
Petrovski, I.G. 69[1]
Pfluger, A. IV 6[2] 48[2] 50[1] 51 106
Poincare, H. 151
Point at infinity 1
Point of linear density 8
Point, regular of a mapping 4
Poisson, S.D. 16 131
Polya, G. and Szegoe, G. 126[1] 133[1]
Pommerenke, C. 117 133[1]
Potential of a constant electric field 156 160
Potential of a constant magnetic field 160
Potential, complex 158
Prime end 46
Principle, majorant, Lehto's 123 126 128 130 132 134
Principle, majorization 117
Quadrilateral 49—51
rectangle 51
Reich, E. IV 50[1] 52—54 80 85 109[2] 112[2] 154 155[3—7]
Reich, E. and Strebel, K. IV[1—3] 52[3] 54[1] 80[2] 85[1—3] 154[3]
Relative electric permeability 157
Renelt, H. IV[1 3] 46[2] 135[1 2] 145[1 3] 149[1 3] 150[4]
Riemann, B. 38 48 80 82 139 149—152 162
Riesz, F. 6
Riesz, M. 16[1 2]
Saks, S. 2 6[1 2] 9[2] 11[2] 109[2]
Saks, S. and Zygmund, A. 2[1]
Scepetev, V.A. 155
Schaeffer, A.C. and Spencer, D.C. IV[1]
Schiffer M. IV[1 2] 52[2] 117 135[2] 144[2] 147 150
Schiffer M. and Schober, G. IV[1 2] 117[1 2 4 5] 150[3 4 6]
Schober, G. IV[1] 117[2] 150[1]
Schwarz, H.A. 6 17 38 55 56 116 122 129 130 138
Schwarzian derivative 134
Sense-preserving homeomorphism 3
Seretov, V.G. 155[1—3]
Set, measurable 1
Shah Tao-shing III[1] IV[1] 53[1] 67[1] 72[1] 102[1] 106 107
Shah Tao-shing and Fan Le-le 106[1] 107[1]
Shibata, K. 155[1]
Sommer, F. 2 47
Soni, A.K. 117
Spencer, D.C. IV
Springer, G. 151[1] 162[1]
Stein, P. 16[1]
Strassmann, F. 164
Strebel, K. IV[2—5] 5[1 6] 52 54 80 84[2] 85 153[2] 154[8] 155[7]
Support of a function 2
Surface, Riemann 149—155 162
Szegoe, G. 126 133
Taari, O. 51[1]
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