Keen L., Lakic N. — Table of Contents Hyperbolic Geometry from a Local Viewpoint :: Электронная библиотека попечительского совета мехмата МГУ

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Keen L., Lakic N. — Table of Contents Hyperbolic Geometry from a Local Viewpoint

Keen L., Lakic N. — Table of Contents Hyperbolic Geometry from a Local Viewpoint

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Название: Table of Contents Hyperbolic Geometry from a Local Viewpoint

Авторы: Keen L., Lakic N.

Аннотация:

Written for graduate students, and accessible to upper-level undergraduates, this book presents topics in two-dimensional hyperbolic geometry. The authors begin with rigid motions in the plane, which are used as motivation for a full development of hyperbolic geometry in the unit disk. The approach is to define metrics from an infinitesimal point of view: first the density is defined and then the metric via integration.

The study of hyperbolic geometry in arbitrary domains requires the concepts of surfaces and covering spaces as well as uniformization and Fuchsian groups. These ideas are developed in the context of what is used later. The authors then provide a detailed discussion of hyperbolic geometry for arbitrary plane domains.

New material on hyperbolic and hyperbolic-like metrics is presented. These are dynamical generalizations of the Kobayashi and Caratheodory metrics for plane domains. This book concludes with applications to holomorphic dynamics, including new results and accessible open problems.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 250

Добавлена в каталог: 23.05.2008

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Предметный указатель

$A(\Omega)$       250
$cK_X^{\Omega}$       196
$cR(X, \Omega)$       184
$glc(X, \Omega)$       183
$glk(X, \Omega)$       180
$gl_{\Omega}(f)$ ,       174
$G_{a, b}$       91 258
$i(\Omega, z)$ , $i(\Omega)$       253
$kR(X, \Omega)$       182
$l(\Omega)$       254
$Q(\Omega)$       249
$R(X,\Omega)$       178
$R(\Omega)$       250
      85
$\Delta*$       73 134 146
$\epsilon$ -bounded      248
$\epsilon(\Omega)$       247 256
$\gamma_1 \equiv \gamma_2$       71
$\lambda(G)$       83
$\lambda(\tau)$       220 263
$\Lambda_0(G)$       87
$\mathcal{H}_l \updownarrow (X, Y)$       153
$\omega(G)$       83
$\Pi_1(X, p)$       71
$\rho_{01}$       220
$\rho_{a, b}$       173 219
$\rho_{F^*}$       115
Accidental cycle      111
Accidental vertex      107
Accumulation points      191
Affine maps      8
Angle condition      112 115
Arc-wise connected -space      72
Asymptotic path      76
Asymptotic value      76
Axis      47
Blaschke product      64 65 210
Bloch condition      178
Bloch constant      178
Bloch subdomain      178
Bounded cross ratio property      248
Caratheodory Bloch subdomain, c-Bloch subdomain      184
Caratheodory contraction constants, global, infinitesimal      183
Caratheodory density      163
Caratheodory density, generalized      166
Caratheodory density, standard      163
Caratheodory Lipschitz .subdomain, c-Lip subdomain      183
Caratheodory Lipschitz domain      183
Caratheodory pseudo-distance      168
Caratheodory — Bloch domain, c-Bloch domain      184
Caratheodory — Lip, c-Lip domain      184
Cauchy — Morera theorem      55
Cauchy — Riemann equations      10
CK-condition      CK6
CK-Lipschitz subdomain, CK-Lip      196
Collar      148
Commutator      85
Compact -subset of a topological space      69
Complete metric space      31
conformal      9
Conformal density      139
Conformal invariant      15 141
Conformally equivalent      59
Congruent      1
Connected topological space      69
Constant curve      71
Contraction properties, infinitesimal and global      172
Convex      27
Coordinate chart      69
Cover      74
Covering space      69 74
Cross ratio      15 38
Curve      6
Cycle relation      111
Cycle transformation      111
Degenerate subdomain      195
Denjoy — Wolff theorem      192
density      11
Dirichlet domain      101
Discontinuous group      83
Discrete group      24
Elementary group      84 90
Elliptic cycle      111
Elliptic function      97 258
Elliptic integrals      96 145
Elliptic pencil      18
Elliptic transformations      20 50
Equivalent densities      245
Equivalent metrics      240
Essential singularity      54
Euclidean density      28
Euclidean geometry      6
Euclidean plane      5
Extremal length      144
F*      115
Free homotopy      73
Free side      113
Free vertex      107
Fuchsian group      25 89
Fundamental domain      98 99
Fundamental group      71
Fundamental polygon      108 109
Gaussian curvature      141
Generalized caratheodory density      166
Generalized Kobayashi density      155
Geodesic ray      35
Geodesic segment      6 36 128
Global contraction      56
Global contraction constants      174 176
Global contraction property      172
Hausdorff space      68 69
Holomorphic map      53
Homotopy class      71
Horoball      48
Horocycle      52
Hurwitz theorem      58
Hyperbolic area      45
Hyperbolic cycle      112
Hyperbolic density      33
Hyperbolic domain      124
Hyperbolic geodesic      35
Hyperbolic line      35
Hyperbolic metric      10

Hyperbolic metric in the disk      32
Hyperbolic pencil      18
Hyperbolic plane      9
Hyperbolic polygon      39
Hyperbolic reflection      51
Hyperbolic rotation      50
Hyperbolic space      82
Hyperbolic transformations      20
Hyperbolic triangle      39
HyperbolicalIy convex      101
Ideal cycle      111
Ideal polygon      39
Ideal triangle      39
Ideal vertex      107 111 113
Infinitesimal contraction      56
Infinitesimal contraction constants      174 176
Infinitesimal contraction property      172
Infinitesimal strict contraction      176 177
Injectivity radius      253
inversion      8
Involution      7
Isolated singularity      53
Iterated function system, forward      191
Iterated function systems, backward      191 195
Iterated function systems, degenerate      195
Jacobi, C.      96 261
k(z)      87
Kleinian group      25
Kobayashi Bloch subdomain, k-Bloch subdomain      182
Kobayashi contraction constants      180
Kobayashi density      154
Kobayashi Lipschitz subdomain, *c-Lip subdomain      180
Koebe domain      134
Koebe-1/4 theorem      67
Liouville theorem      55
Lipschitz domain      177
Lipschitz subdomain, Lip-subdomain      177
Local uniform convergence      58
Locally finite      105 106
Loxodromic transformations      20
Marking generators      142
Markowsky, G.      162 171
Maskit, B.      151
Maximum principle      55
Meromorphic      53
Metric space      6
Modular group      262
Modulus of a rectangle      145
Modulus of a torus      142
Modulus of an annulus      147
Moebius group      14
Moebius transformations      14
monodromy      76
Monodromy group      97
Monodromy theorem      77
Montel's theorem      59
Multiplier      20
Nomotopic      70
Nomotopic curves      59 71
Normal family      58
O(G)      84
Orbifold      89
Orbit      84
Pair density      220 240
Parabolic cycle      112
Parabolic transformations      21
Poincare polygon theorem      115 123
Poincare, H.      97
Pole      54
Product curve      70
Pseudo-metric      168
PSL(2,C)      23
PSL(2,R)      23
Quasi-doubly periodic      262
Quasi-hyperbolic density      245
Quotient surface      88
Radial projection      34
Rational map      63
Ray      6
Reflection      7 51
Regular covering      75
Regular set      83
Relator in a group      111
Removable singularity      54
Riemann map      62
Riemann mapping theorem      60
Riemann sphere      12
Riemann surface      68 69
Rigid motions      7
Rotations      7
Scaling map      8
Schwarz lemma      55
Schwarz reflection principle      63
Schwarz — Pick Lemma      56
Separating annulus      249
Side-paired polygon      107
Side-pairings      107
Similarities      8
Simply connected      59 72
Smooth covering space      74
Smooth surface      69
Spherical distance      30
Stereographic projection      12
Strict contraction      176 177
Strictly uniform      175
Theta function      222 261
Topological rectangle      144
Topological space      68
Trace      18
Translation length      47
Translations      7
Trivial group      72
Uniformization theorem      81
Uniformly bounded cross ratio      248
Uniformly perfect domain      245
Uniformly thick domain      254
Univalent map      67
Universal cover      60
Universal covering group      80
Universal covering space      77 80
Upper-semi-conlinuous function      160
V(G)      87
Weierstrass $\wp$ -function      259
Weierstrass theorem      58

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