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| Courant R. — Dirichlet's Principle, Confomal Mapping and Minimal Surfaces |
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| Предметный указатель |
Schwarz 96 199
Schwarz — Cayley differential parameter 276
Schwarz' chains 208
Schwarz' inequality 14
Semicontinuity 104ff.
Semicontinuity of Dirichlet’s integral for harmonic functions 11
Semicontinuity, lower 23
Sewing theorem 69
Shiffman 4 200
Slit domain 45ff. 143
Slit domain with boundary of non zero content 60
Slit domain, characteristic number of 82
Slit domain, definition 45
Slit domain, half-plane 46 61 85
Slit domain, mapping of domain of infinite connectivity on 58
Slit domain, mapping of domain of infinite genus on 92
Slit domain, mapping of Klein bottle on 82 90
Slit domain, mapping of multiply connected do main on 308
Slit domain, mapping of plane domain on 55
Slit domain, mapping of projective plane on 82 90
Slit domain, mapping of Riemann domain of higher genus on 85
Slit domain, mapping of torus on 82. 90
Slit domain, non-orientable 81
Slit domain, normalization of 92
Slit domain, not of genus zero 80
Slit domain, radial 265ff.
Slit domain, ring 265ff.
Slit domain, topological structure of 81
Slit domains, conformally equivalent 92
Smoothing process 24
Soap film experiments 3 119ff. 141ff. 160
Soap film experiments, solve Plateau’s problem 96
Stationary point, unstable 223
Stationary vector, definition 110
Stationary vector, represents minimal surface 112ff.
Streamlines 39 46 86
Streamlines, exceptional 46
| Surface, closed, topological characterization of 82
Surfaces of lower type 142
Three point condition 103 104
Tompkins 4 134 200
Tonelli 100
Torus, mapping on slit domain of 82 90
Transversality 207 218
Triangle inequalities 14
Triangulation 77
Uniformization 77
Uniformization of general Riemann domains 75
Uniqueness question for Plateau’s problem 119
Uniqueness theorems for conformal mapping 187ff.
Uniqueness theorems for conformal mapping on classes of plane domains 188
Uniqueness theorems for conformal mapping on domains containing the point at infinity 190
Uniqueness theorems for conformal mapping on Riemann surfaces with branchpoints 188
Univalent functions 276ff.
Univalent functions, coefficient problem for 300ff.
Univalent functions, connection with conformal mapping 276ff.
Unstable stationary point 223
Variables, local complex 66
Variation of Dirichlet’s integral for harmonic vectors 110
Variation of Green’s function 292ff.
Variation of minimal surface 110
Variation of parameter representation of minimal surface 108
Variation, boundary 306ff.
Variation, first, second see "Dirichlet’s integral"
Variation, interior 298ff.
Variational conditions 169 179 184
Variational problems for mapping theorems in two dimensions 192
Variational problems for minimal surfaces 101
Variational problems for multiply connected minimal surfaces 144ff.
Vortex Motion 39
Weierstrass 96
Weierstrass’ theorem 23
Wiener 120
Wirtinger 270
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