Seppala M. — Geometry of Riemann surfaces and Teichmuller spaces :: Электронная библиотека попечительского совета мехмата МГУ

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Seppala M. — Geometry of Riemann surfaces and Teichmuller spaces

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Название: Geometry of Riemann surfaces and Teichmuller spaces

Автор: Seppala M.

Аннотация:

This monograph grew out of a series of lectures held by the first author at the University of Regensburg in 1986 and in 1987 and by the second author at the University of Joensuu in 1990. This book would presumably not have been written without the initiative of Professor Leopoldo Nachbin.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 269

Добавлена в каталог: 23.10.2010

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Предметный указатель

$Aut_{0}(F)$ , inner automorphisms of a topological group      165
$Diff(\Sigma)$       145
$Diff_{+}(\Sigma)$       145
$D^{(-1,1)}(G)$ , differentials of a group      143
$D^{(-1,1)}(X)$ , (-1,1) differentials of X      142
$Homeo(P^{2})$       139
$Homeo_{0}(P^{2})$       139
$M(P^{2})$       140
$M(\Sigma)$ , moduli space      146
$M^{g}M(\Sigma)$ , moduli space      146
$P^{2}$ , pair of pants      137
$T(\Sigma)$ , Teichmueller space      145
$T^{g}T(\Sigma)$ , Teichmueller space      145
$\Gamma(\Sigma)$ , modular group      146
$\Gamma^{g}\Gamma(\Sigma)$ , modular group, mapping class group      146
$\mathcal{E}$ , elliptic      24
$\mathcal{H}$ , handle      24
$\mathcal{H}$ , handle, boundary      27
$\mathcal{H}$ , handle, interior      28
$\mathcal{H}$ , handle, real handle      28
$\mathcal{M}(P^{2})$       137
$\mathcal{M}(\Sigma)$ , complex structures      145
$\mathcal{P}$ , pants      24
$\mathcal{P}$ , pants, boundary      26
$\mathcal{P}$ , pants, interior      26
$\mathcal{R}^{0}(G,PGL(2,R))$ , deformation space of groups      153
$\overline{\partial}$       141
$\partial$       141
$\Sigma^{c}$ , complex double      149
Abelian differential periods      147
Absolutely continuous      63
ACL (absolutely continuous)      63
Ahlfors, L.V.      59 65 140 147 192
Ailing, N.      184
Algebraic curves, complex      185
Algebraic curves, real      185
Andreotti, A.      207
Annulus, Teichmueller space of      152
Atlas      70
Atlas, complex analytic      70
Atlas, dianalytic      70
Atlas, orientable      70
Aut(F), continuous automorphisms of a topological group      165
Automorphisms of $\Sigma$ , action on the space of compl. structures      145
Baily, W.L.      205
Base point of a pants decomposition      188
Bel(G), Beltrami differentials of G      143
Bel(X), Beltrami differentials of X      142
Beltrami differential on a Klein surface      142
Beltrami equation      64
Bers, L.      65 192 206
Biholomorphic mapping      66
Boundary      70
Branch number      97
Branch point      97
Branching number, total      98
Brumfiel, G.      164
Bujalance, E.      100
Buser, P.      115 117
Cartan, H.      205
Chen Min      12
Circular distortion      62
Collar      110
Collar Lemma      115
Collar, $\mu$ -collar      110
Collar, area      110
Collar, boundary, inner boundary component      113
Collar, boundary, outer boundary component      113
Collar, width      110
Commutator      29
Commutator, matrix of      131
Complex dilatation      64
Complex double      149
Coordinate      23
Coordinate chart      69
Coordinate transition function      70
Covering, orientable      77
Cross cap      80
Curve      72
Curve, closed      76
Curve, end-points      72
Curve, one-sided      76
Curve, simple closed      76
Curve, two-sided      76
Curves, homotopic      86
Decomposing curve of a pants decomposition of a stable surface      187
Decomposing curves      119
Decomposing node of a pants decomposition of a stable surface      187
Decomposition into pairs of pants of a stable surface      187
Deformation space of a group in a topol. group      164
Deformation space of groups      153
Dehn twist, left Dehn twist      95
Derivates, $L^{p}$       64
Differential (-1,1) on a Klein surface      142
Differential Beltrami      64
Dilatation quotient      63
Dilatation, complex      64
Dilatation, complex, transformation      65
Dilatation, maximal      61
Direct sum      80
Dirichlet polygon (of a Fuchsian group)      85
Discontinuous      82
Discrete (group)      82
Disk on a Riemann surface      110
Distortion, circular      62
Double, complex      77
Doubly connected surfaces moduli      137
Dual (of a Banach space)      66
Earle, C.      148 207
Elliptic modular function      181
Elliptic modular group      181
Epstein, D.B.A.      123
Etayo, J.J.      100
Euler characteristic      76
Existence Theorem (of quasicon-formal mappings)      65
Extremal Mapping Theorem      140 144
Fenchel — Nielsen coordinate      190
Fenchel — Nielsen coordinate, gluing angle      190
Fenchel — Nielsen coordinate, length coordinate      190
Fenchel — Nielsen coordinate, modified      191
Fricke, L.      3
Fuchsian group of the first kind      107
Fuchsian group of the second kind      107
Fuchsian group, Dirichlet polygon      85
Fuchsian group, fundamental domain      85
Fuchsian group, Poincare polygon      85
Fundamental domain (of a Fuchsian group)      85
Fundamental group      87
Gamboa, J.M.      100
Gardiner, F.P.      148 164 204
Gauss — Bonnet formula      96
Genus      43 76 77
Genus of a surface with nodes      185
Genus, arithmetic      77
Geodesic curves, distance between      111
Geodesic length function      158
Geodesic length function, continuity      159
Geodesic length function, parametrization of the Teichmueller space by      161
Geodesic length function, real analyticity      160
Geometric invariant theory      205
Gieseker, D.      205
Glide-reflection      16
Gluing angle      190
Gordan, P.      100
Gromadzki, G.      100
Group, Beltrami differential      143
Group, compact type      43
Group, differential      143
Group, discontinuous      82
Group, discrete      82

Group, Kleinian      82
Harris, J.      206
Helling, H.      164 170 171 174 175 245
Herrlich, F.      206
Holm, P.      207
Holomorphic function between Banach spaces      66
Homeomorphism, analytic      70
Homeomorphism, dianalytic      70
Homeomorphism, holomorphic      70
Homotopy classes      87
Homotopy group      87
Horocycle      103
Hurwitz theorem      97 99
Hurwitz, A.      97—99
Hyperbolic angle      211
Hyperbolic area      96
Hyperbolic circle, length      212
Hyperbolic disk, area      212
Hyperbolic metric      33
Hyperbolic metric, curvature      210
Hyperbolic metric, definition      210
Hyperbolic metric, distance between points      210
Hyperbolic metric, intrinsic      96
Hyperbolic metric, isometries      211
Hyperbolic metric, Riemann surfaces      96
Hyperbolic ray      211
Hyperelliptic Riemann surface      162
Index of orientability      78
Involution      77
Isometric circle      25
Isometric Riemann surfaces      117
Isomorphism, geometric      23 153
Isomorphism, induced      20
Isomorphism, type-preserving      20
Isospectric Riemann surfaces      117
Keen, L.      115
Klein bottle      72
Klein bottle, Teichmueller space of      152
Klein surface, classical      71
Klein surface, non-classical      71
Klein, F.      3 5 208
Kleinian group      82
Klein’s quartic      100
Klein’s Riemann surface of genus 3      100
Knudsen, F.      205
Kra, I.      132 135
Kravetz, S.      164
Kulkarni, R.      100
L(G) of limit points of G is the limit set limit set      107
L-invariant      51
Lehner, J.      3
Lehto, O.      59 140 204
Lehtonen, A.      72 73 81
Length coordinate      190
Limit set of a Fuchsian group      107
Mapping class group of a surface      146
Mapping class group, discreteness of the action      163
Mapping, biholomorphic      66
Mapping, quasiconformal      61
Maximal dilatation      61
McKean, H.P.      117
Metric of a stable surface      186
Modular function, elliptic      181
Modular group of a surface      146
Modular group, discrete orbits      163
Modular group, discreteness of the action      163
Modular group, elliptic      181
Moduli problem      71 137
Moduli space of a surface      146
Moduli space of pairs of pants      140
Moduli space of real curves      195
Moduli space of stable Riemann surfaces      189
Moduli space of stable Riemann surfaces topology      193
Moduli space of stable Riemann surfaces, projectivity      205
Moduli space of symmetric stable Riemann surfaces topology      197
Moduli space of the torus, compactification      183
Moduli space of the torus, isomorphic to C      182
Moduli space, algebraic structure      205
Moduli space, complex structure      205
Moebius strip      72
Moebius strip, Teichmueller space of      152
Moebius transformation, conjugate      14
Moebius transformation, covering a homotopy class      88
Moebius transformation, elliptic      14
Moebius transformation, glide-reflection      16
Moebius transformation, hyperbolic      13
Moebius transformation, hyperbolic, attracting fixed point      13
Moebius transformation, hyperbolic, axis      13
Moebius transformation, hyperbolic, L-invariant      51
Moebius transformation, hyperbolic, multiplier      13
Moebius transformation, hyperbolic, repelling fixed point      13
Moebius transformation, loxodromic      17
Moebius transformation, orientation preserving      12
Moebius transformation, orientation reversing      12
Moebius transformation, parabolic      14
Moebius transformation, parabolic, horocycle      103
Moebius transformation, reflection      16
Moebius transformation, type      12
Morgan, J.      164
Mumford, D.      205
Nag, S.      204
Natanzon, S.      208
Neighborhood, $\epsilon$ -distance      109
Nielsen Criterium      6
Nielsen, J.      6 106 153
Nielsen’s Theorem      153
Node      185
Non-Euclidean line      12
Non-Euclidean line, oriented      48
normalizer      198
Orientation      70
Orthogonal decomposition      46
Pair of pants, general      117
Pair of pants, standard      117
Pairs of pants, degenerate      187
Pants decomposition      118
Pants decomposition, geodesic      188
Parametrization problem      23
Part of a nodal surface      185
Picard group      83
Poincare polygon (of a Fuchsian group)      85
Principal-circle group      23
Principal-circle group, primary element      33
Principal-circle pair      24
Properly discontinuous group      82
Pull back of a pants decomposition      189
Quadrilateral      59
Quadrilateral, modulus      60
Quasiconformal mapping      61
Quasiconformal mapping of a Klein surface      141
Quasiconformal mappings, existence and uniqueness      142
Quasiconformal mappings, uniqueness      65
Ramification number      97
Real curve, moduli space      195
Real projective plane      71
Reflection      16
Regular set      82
Riemann mapping theorem      86
Riemann moduli problem      137
Riemann moduli space      140
Riemann surface, doubly connected, moduli      137
Riemann surface, isometric      117
Riemann surface, isospectric      117
Riemann surface, non-classical, moduli space      195
Riemann — Hurwitz relation      98
Riemann, B.      98
Ring domain      60
Ring domain, moduli      137
Ring domain, modulus      60
Ringed space      148

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