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Jost J., Simha R.T. — Compact Riemann Surfaces: An Introduction to Contemporary Mathematics
Jost J., Simha R.T. — Compact Riemann Surfaces: An Introduction to Contemporary Mathematics

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Название: Compact Riemann Surfaces: An Introduction to Contemporary Mathematics

Авторы: Jost J., Simha R.T.

Аннотация:

Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory. The analytic approach is likewise new as it is based on the theory of harmonic maps. For this 2nd edition the author has further improved aspects of presentation of various parts of the text.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd edition

Год издания: 2002

Количество страниц: 292

Добавлена в каталог: 22.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel's theorem      254 264 267
Addition theorem for elliptic functions      267
Adjoint      199
Ahlfors — Schwarz lemma      66 68
Algebraic curve      245
Algebraic equation      242 244 246
Algebraic function-field      248
Algebraic space-curve      246
Analytic      19
angle      24
Annulus      74
Anticonformal      121
Area      23
Arzela — Ascoli theorem      110
Ascoli — Arzela theorem      168
Atlas      1 19
Banach fixed point theorem      91
Banach space      81
Banach-Saks theorem      86
Bergman-metric      222
Biholomorphic      27 69
Bolyai      33
Boundary value problem      102
Branch point      64
Branched covering      241
Brill — Noether reciprocity theorem      222
Canonical bundle      232
Canonical curve      235
Canonical divisor      211 212 217 231 235
Canonical homology basis      195 205 209 258
Canonical map      235 238
Chain      190
Change of coordinates      24
Chart      1
Chern class      229
Closed      189—192
co-closed      199
Co-exact      200
Cohomologous      203
Cohomology class      63
Commutator subgroup      195
complete      23 29 70 74
Complex manifold      235
Complex projective space      234
Complex structure      197
Complex torus      205
conformal      19 21 24 121
Conformal atlas      19 55
Conformal factor      24
Conformal invariance      19
Conformal maps      19
Conformal Riemannian metric      22 25 34 232
Conformal structure      19 67 155 156 161
Conformal structures on tori      77
Congruence subgroup      80
Conjugation operator      198
Contraction principle      91
Convex      44 137
coordinates      1
Courant — Lebesgue lemma      126
Covariant Hessian      137
Covering      7 8
Covering transformation      12 21
Curvature      24 29 30 59 63 66—68 74 141 145 184 222 224 232
Curve      3 240
CYCLE      190
De Rham cohomology group      190 197
de Rham's theorem      197
Degree      64 66 150 189
Degree of a divisor      212
Degree of a line bundle      231
Dehn twist      183
Derivative      91
Diffeomorphism      2 145 152 163 184
Difference quotient      98
Differentiable      1 2
Differentiable manifold      1
Differentiable structure      1
Differential form      189
Differential of the first kind      207
Differential of the second kind      207
Differential of the third kind      207 256 258 259
DIMENSION      1
Dirichlet fundamental polygon      44
Dirichlet integral      102
Dirichlet principle      102 104 123 204
Distance      23
Distance-decreasing      69
Divisor      211 224 226 228 255 267
Dominate      10
Dual      190 192
EDGE      34
Effective      28 211 215 228 236 260 267
Elementary symmetric function      242
Elliptic      43 236
Elliptic curve      262 264
Elliptic function      263
Elliptic geometry      26 33
Embedding      235 238 247
Energy      31 121
Energy functional      31
Energy integral      120
Entire holomorphic function      72
Equivalent coverings      10
Euclidean algorithm      249
Euclidean geometry      33
Euclidean motions      48
Euclidian metric      24 25
Euler characteristic      58 61 63
Exact      189—192
Exponential map      35
Extended complex plane      20
Exterior derivative      189
Exterior differential form      189
Exterior product of differential forms      196
Faithful      28
Fenchel — Nielsen coordinates      174 180 183
Field of meromorphic functions      247 248
Field of rational functions      245 249
First Chern class      229
First Chern form      229
First cohomology group      195
First homology group      194 195
Fixed model      162
Fixed point      42
Frechet differentiable      91
Frobenius' Theorem      191
Fundamental 2-form      198
Fundamental domain      44 46 75
Fundamental group      4 5 54 77 195
Fundamental polygon      44 48 60 207 209
Gauss      33 155
Gauss — Bonnet formula      59 66 148
Gauss — Bonnet theorem      33 62 176 232
Genus      58 61 161 184 194 224 235
Geodesic      31 34—36 38 39 43 134 142 174
Geodesic line      31
Geodesic polar coordinates      37
Geodesic polygon      60
Geodesic triangle      60
Glueing lemma      180
Great circles      33
Green function      112
Green's identity      106
Group of transformation      28
Group structure of an elliptic curve      265
Harmonic      19 21 72 79 102 107 109
Harmonic conjugate      22
Harmonic function      22 104 109 110
Harmonic I-form      200—202 204
Harmonic map      79 124 126 143 145 150 163 184
Hausdorff      1
Hausdorff property      224
Hausdorff space      11
Hermitian metric      228 232
Hexagon      48
Hilbert space      81 94 104 198
Hoelder continuous      113 160
Holomorphic      19 21 26 63
Holomorphic 1-form      200 205 207 210 221 222 231
Holomorphic function      19
Holomorphic quadratic differential      162 164 172 185 219 222 237
Holomorphic section      227
Holomorphic tangent bundle      232
Homeomorphism      2
Homogeneous coordinates      234 246
Homology group      190
Homotopic      3 77 132 162
Homotopy      8
Homotopy class      4
Homotopy of curves      3
Hyperbolic      43 47
Hyperbolic area      59
Hyperbolic geometry      26 33
Hyperbolic hexagon      176
Hyperbolic metric      25 29 30 32 42 59 126 135 144 161 174
Hyperbolic surface      163
Hyperbolic triangle      59
Hyperelliptic      236 238 254
Hyperelliptic involution      254
Implicit function theorem      91 168 261
Integration by parts      93
Intersection      193
Intersection number      194 196
Intersection pairing      196
Isometry      24 161
Isometry group      29
Isomorphic line bundles      226
Isotropy group      28
Jacobi inversion theorem      259
Jacobi variety      267
Jacobian variety      205 254
Kaehler form      198
Klein      245
Kneser      153
Kobayashi-hyperbolic      68
Laplace operator      102 157
Laplace — Beltrami operator      24 199
Lattice      75 205 262 263
Laurent expansion      206 238
Length      23 29 31 36 154
Lift      12
Line bundle      225 227 228
Linear transformation      240
Linearly equivalent      212 217 259 267
Lipschitz continuous      113
Lobacevsky      33
Local diffeomorphism      7
Local form of a holomorphic function      20
Local homeomorphism      7 21
m-canonical form      236
Manifold      1
Marked torus      78
Marking      162
Mean value inequality      112
Mean value theorem      106 107 114
Measurement      155
Meromorphic      74
Meromorphic function      19 207 211 213 236 242 244 255 259
Meromorphic I-form      206 211
Meromorphic section      227 228
Metric      23 28 197 222 224
Metric fundamental polygon      44 48
Metric surface      34 39
Metric topology      23
Minimizing sequence      102
Mobius transformation      26 27 30 46 240
Modular group      75
Moduli space      78 161 162
Mollification      88 111
Montel's theorem      74
Multiple of a divisor      211
Newtonian potential      119
Non-Euclidean      26
normal      74
Normal subgroup      12
Null- homotopic      6
Null-homologous      192
Orbit      41
Order of ramification      64
Orientable      55 193
Orientation      55
Orthogonal      82
Orthogonal complement      82
Orthogonal decomposition      201
Orthogonal projection      83
Orthonormal sequence      86
Pair of pants      174
Parabolic      43 46
parallel      33
Parallelogram law      82
Parametrized proportionally to arclength      31 32
Path      3
Period      74 254
Period matrix      205 209 210
periods      205 207 209
Picard group      226
Picard theorem      73
Plane algebraic curve      262 263
Plane curve      246
Poincare duality      196 229
Poincare inequality      100 103 104
Poincare lemma      191
Poincare's model      26
Poisson equation      104
Polygon      34
Potential      23 29
Principal divisor      211
Properly discontinuous      41
Properly discontinuously      13
Quotient topology      42
Ramification point      64
Rational function      242
Reciprocity laws      209
Rectifiable      19
Rectifiable curve      23
Removable singularities      20
Residue      206 257 259
Riemann      243 245
Riemann surface      39 42 55 156 161 184 197 224 235 243—245
Riemann — Hurwitz formula      64 217 222 234 241 246 247 264
Riemann's Bilinear Relations      210
Riemann-Roch theorem      186
Riemann-Roch theorem, Riemann surface      19
Riemannian metric      154
Riesz representation theorem      83
Scalar product      81 198
Schottky double      187
Schwarz inequality      81
Schwarz lemma      26
Secant      240
Second variation      140 142
Sheaf theory      17
Simply connected      22
Simply-connected      6 7 11 22
Smoothing      88 202
Smoothing function      88
Sobolev space      93 94 97
Sphere      2 30 33
Stability lemma      105
1 2
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