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Buser P. — Geometry and spectra of compact riemann surfaces
Buser P. — Geometry and spectra of compact riemann surfaces

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Название: Geometry and spectra of compact riemann surfaces

Автор: Buser P.

Аннотация:

This monograph is a self-contained introduction to the geometry of Riemann Surfaces of constant curvature -1 and their length and eigenvalue spectra. It focuses on two subjects: the geometric theory of compact Riemann surfaces of genus greater than one, and the relationship of the Laplace operator with the geometry of such surfaces. The first part of the book is written in textbook form at the graduate level, with few requisites other than background in either differential geometry or complex Riemann surface theory. It begins with an account of the Fenchel-Nielsen approach to Teichmüller Space. Hyperbolic trigonometry and Bers’ partition theorem (with a new proof which yields explicit bounds) are shown to be simple but powerful tools in this context. The second part of the book is a self-contained introduction to the spectrum of the Laplacian based on head equations. The approach chosen yields a simple proof that compact Riemann surfaces have the same eigenvalues if and only if they have the same length spectrum. Later chapters deal with recent developments on isospectrality, Sunada’s construction, a simplified proof of Wolpert’s theorem, and an estimate for the number of pairwise isospectral non-isometric examples which depends only on genus. Research workers and graduate students interested in compact Riemann surfaces will find here a number of useful tools and insights to apply to their investigations.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 453

Добавлена в каталог: 19.06.2006

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$S^{1}$      21
$\mathcal{B}_{s}$      172
$\mathcal{C}(M)$      229
$\mathcal{F}_{2}$      171
$\mathcal{M}_{2}$      154
$\mathcal{R}_{s}$      211
$\mathcal{T}_{s}$      139 0 29 144 147
$\mathfrak{M}_{2}}$      154
$\nu$-Cauchy sequence      363
$\nu$-convergence      363
$\nu$-equivalcm      363
$\omega_{0}$      141
1—homeomorphism      83 134 410
1—product      363
Abel transform      194 196 200
Admissible, Jordan curve      376
Admissible, list for graph      79
Admissible, sequence for isospectraltiy      335
Admissible, set for homotopy      19
Admissible, transform pair      252
Alexander — Tictze theorem      410
Almost conjugate      285
angle      34
Angle of cone-like singularity      313
Angle type      35
Angle, subsequent      34
Arzctt — Ascoli theorem      429
Asymptotic equality      235
Atlas, confonnal      29
Atlas, hypcrbolic      6
Axis      171 227
Baer — Zieschang theorem      411
Base surface for markings      71 138 140 336 384
Bers coordinates      172 174
Bers’ constant      123
Bers’ theorem      123 124 125 130
Boundary orientation      11
Boundary point      4
Boundary point at infinity      4 22 50
Boundary point, ordinary      6
Boundary twist      425
Building block      30 63 302 305
Canonical, curve system      141
Canonical, dissection      166
Canonical, generators of Fuchslan group      171
Canonical, polygon      168
Canonical, polygon, normal      383
Cayley graph      297
Cell structure of Teichmueller space      144 334
Chebyshev functions      243 245 246
Cheeger’s constant      215
Circle sector      6
Cleaning option      430
Closed geodesic      22
Closed geodesic, iterate      22
Closed geodesic, non-oricnted      269 291
Closed geodesic, norm      245
Closed geodesic, one-sided      26
Closed geodesic, oriented      22 227 229
Closed geodesic, prime      22 228 245
Closed geodesic, primitive      22 228 291
Co-area formula      217
Collar      70 94 343
Collar theorems      94 97 106 112
Collar, width of      70
Colligation in quaternion algebra      53
COLOR      298
Commensurable      336
Complete sequence      379
Completely multiplicative      242
Complex differentiable      380
Cone-like singularity      159 313
Conformal structure      29 139 156
const      204
Convolution      259
Coordinate maps for TeichmUller space      147
Coordinates, $L-V-C$      169
Coordinates, Bers      172 174
Coordinates, Fenchcl — Nielsen      29 87 147
Coordinates, Fermi      4
Coordinates, Fricke      179
Coordinates, horocyclic      5 198
Coordinates, polar      3
Coordinates, quadrilateral      385
correlated      292
Counterclockwise      58
Curve system, canonical      141
Curve, piecewise regular      375
Cusp      25 111
Cut open      15
CYCLE      313
Dchn — Nidsen theorem      171
Defining relation      164 171 179
Delm twist      72 425
DIRECT      56
Dirichlet series      225 247
Dirichlet, domain      221
Dirichlet, fundamental domain      205
Displacement length      171 175 227 292
Dissection, canonical      166
Dissection, normal canonical      166
Distance in graph      221
Distance in TeichmUller space      152 153
Distance, hyperbolic      2 38 59 198
Domain of operator      370
Domain of sesquilincar form      370
Edge of graph      78 298
Eigenfunction      187
Eigenfunction, radial      198 236
Eigenspace      191 295 296
Eigenvalue      187
Eigenvalue, isolated      378
Eigenvalue, small      210
Endpoint at infinity      22
Endpoint of geodesic      109
Equivalence of canonical dissections      166
Equivalence of closed geodesics      229
Equivalence of homeomotphisms      154
Equivalence of marked Fuchsian groups      171 334
Equivalence of marked Ricmann surfaces      139 145 147
Equivalence of marked Y-picces      67
Equivalence of normal canonical polygons      168
Equivalence of parametrized geodesics      21 22
Equivalence of vectors      49
Equivalence of vertices      313
Equivalence of words      92
Equivalence, Gassmann      285
Equivalence, relation for pasting      8 9
Equivalence, weak      269 291
Euler product      242 243
EXPONENT      287
Fenchcl — Niclscn parameters      29 82 147
Fermi coordinates      4 70
Fermi coordinates on cylinder      10
Fermi coordinates, distance formula      38
Fermi coordinates, sign conventions      4
Figure eight geodesic      86 100 159 272
Fixed point, attractive      172
Fixed point, repulsive      172
Fourier transform      252 258 259
Fpstcin — Zieschang theorem      411
Frickc-coordinaies      179
Friedrichs extension      368
Fuchsian group      170
Fuchsian group, marked      170 171
Fundamental domain      230
Fundamental domain in Telchmueller space      67
Fundamental domain, Dirichlet      205
Fundamental domain, rough      161
Gel’fand conjecture      183 269
General sine and cosine law      61
Generalized triangle      36
Generating function      205
Generating function, decay condition      205
Generating function, induced kernel      206
Geodesic in the quaternion model      49
Geodesic, figure eight      272
Geodesic, loop      26
Geodesic, polygon (curve)      34
Geodesic, polygon (domain)      3
Geodesic, prime      228 245 291
Geodeslc-like      49
Geometric spectrum      235
Gradient      185 363
Graph, 3-regular      79
Graph, connected      79
Graph, cubic      78
Graph, mariced      79
Graph, quotient      298
Green’s formula      185 363
Hairy torus      131
Half-disk      6
Half-edge      79
Heat equation      186 188
Heat equation, fundamental solution      186
Heat equation, solution      188
Heat kernel      185 186
Heisenberg group      287
Hexagon      40
Hexagon, self-intersecting      42
Hilbert — Schmidt theorem      187
Holomorphic      380
Holomorphic family of bounded operators      381 393
Holomorphic family of closed operators      397
Holomorphic family of Laplacians      399
Holomorphic family of matrices      402
Homotope (as verb)      18 73
Homotopicaily trivial      21
Homotopy with gliding endpoints      18
Homotopy, free      21
Homotopy, length-decrcasing      430
Horocyclc      5 25
Hubert theorem      229
Hurwitz’ theorem      159
Hyperbolic plane, disk model      2
Hyperbolic plane, Polncard model      2
Hyperbolic plane, quaternion model      52
Hyperbolic, atlas      6
Hyperbolic, cylinder      9 10
Hyperbolic, distance      2 38 59 198
Hyperbolic, structure      7
Hyperbolic, surface      7
Hyperboloid      32 49
Hypergeometric function      263 264
Incidcnce relations in the quaternion model      50
Induced kernel      206
Infinity-like      49
Injcctivity radius      96
Integral logarithm      257
Interior      6
Intersection, removable      417
Intersection, transversal      416
Irreducible      404
Isomorphism of graphs      80 298
Isomorphism, strong      298
Isopcrimetric, constant      215
Isopcrimetric, quotient      212
Isospcctral      183
Isotopy      83 410 425
Isotopy with poimwise fixed set      410
Isotopy, level-preserving      410
Iterate of closed geodesic      22 228
Jordan — Schocnflies theorem      413
Laplace operator      184 366
Laplace operator, holomorphic family      399
Lattice point problem      22
Length distortion      68 152
Length of cyclc      314
Length of prime number      284
Length spectrum      183 226 229 269
Length spectrum, primitive      229
Length trace formula      230
Let go      18
Lift of prime geodesic      291
Lipschitzian      428
Local, analytic variety      270
Loop      20
Loop, gcodesic      26
Loop, simple      20
LSP      269
M-O-S      248
Mahler compactness theorem      163 273
Mapping class      154
Mapping class group      154
Marking equivalence of Fuchsian groups      171 334
Marking equivalence of P-pieces      67
Marking equivalence of Riemann surfaces      139 145 147
Marking homeomorphism      139 143
Marking of Fuchsian group      170 171
Marking of K-piece      67
Marking of Ricmann surface      139
Marking of X-piece      70
Mercer's theorem      187
Metric tensor      184 185
Minimax principles      213
Moduli problem      67 160
Moduli space      161 211
Neumann problem      215
Non$\pm$homotopic      411
Non-solitary      284
Norm in quaternion algebra      53
Norm of closed geodesic      245 253
Norm of operator      370
Normal canonical      337
Normal canonical, dissection      166
Normal canonical, generators of Fuchsian group polygon      168 383
Normal form presentation of surface      164
Normal, neighborhood      429
Oassmann equivalent      285
One-sided      26
Operator, bounded      370
Operator, bounded inverse      370
Operator, closed      370
Operator, domain of      370
Operator, linear      370
Operator, range of      370
Operator, sum      370
Order of cone-like singularity      313
Order of cycle      314
Orientation of edge in graph      299
Orientation of graph      298
Orientation of surface      7
Overlap      416
Overlap, free      422
Overlap, proper      416
p(n)      291
Pair of pants      63
Pair of pants in standard form      64
Pair of pants, degenerate      109
Parallel curve      135
Parameter geodesic      82 341
Parity of configuration      59
Partition      123
Pasting      8
Pasting condition      8 9 64
Pasting of dosed geodesics      10
Pasting scheme      9 82 143 164
Pentagon      39
Piecewise circular      135
Point at infinity      4 22
1 2
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