Lars Valerian Ahlfors: Collected Papers Volume 1 1929-1955 Rae Michael Shortt Assistant Editor Birkhäuser Boston Basel Stuttgart 1982
LARS VALERIAN AHLFORS: COLLECTED PAPERS CONTENTS-Volume 1 About the Organization of These Volumes Author's Preface Publications of Lars V. Ahlfors Commentary 1 [1] Sur le nombre des valeurs asymptotiques d'une fonction entiere d'ordre fini (1929) 3 [2] Über die asymptotischen Werte der ganzen Funktionen endlicher Ordnung (1929). 5 [5] Untersuchungen zur Theorie der konformen Abbildung und der ganzen Funktionen (1930) 18 Papers 56 [3] Sur quelques proprietes des fonctions meromorphes (1930) 57 [4] Beiträge zur Theorie der meromorphen Funktionen (1930) 60 [7] Ein Satz von Henri Cartan und seine Anwendung auf die Theorie der meromorphen Funktionen (1931) 65 Commentary 84 [6] Zur Bestimmung des Typus einer Riemannschen Fläche (1931) 86 [17] Sur le type d'une surface de Riemann (1935) 91 [20] Über eine Klasse von Riemannschen Flächen (1936) ' 94 Papers 100 [10] Über die asymptotischen Werte der meromorphen Funktionen endlicher Ordnung(1932) 101 [12] Ein Satz über die charakteristische Funktion und den Maximalmodul einer meromorphen Funktion (1932) 107 Commentary 111 [11] Über eine in der neueren Wertverteilungstheorie betrachtete Klasse transzendenter Funktionen (1932) 112 Commentary 144 [8] Sur une generalisation du theoreme de Picard (1932) 145 [9] Sur les fonctions inverses des fonctions meromorphes (1932) 149 [13] Quelques proprietes des surfaces de Riemann correspondant aux fonctions meromorphes (1932) 152 [14] Über die Kreise die von einer Riemannschen Fläche schlicht überdeckt werden (1933) 163 Page iv xi xv Contents v
[15] Sur les domaines dans lesquels une fonction meromorphe prend des valeurs appartenant a une region donnee (1933) 174 Commentary 189 [16] Über eine Methode in der Theorie der meromorphen Funktionen (1935) 190 Paper 204 [18] Über die konforme Abbildung von Überlagerungsflächen (1935) 205 Commentary 212 [19] Zur Theorie der Überlagerungsflächen (1935) 214 Commentary 252 [22] Über die Anwendung differentialgeometrischer Methoden zur Untersuchung von Überlagerungsflächen (1937) 253 [24] Geometrie der Riemannschen Flächen (1937) 268 Commentary 278 [23] (WithH. Grunsky) Über die Blochsche Konstante (1937) 279 Commentary 282 [26] Zur Uniformisierungstheorie (1939) 283 [28] Die Bergründung des Dirichletschen Prinzips (1943) 297 [32] Das Dirichletsche Prinzip (1947) 313 Commentary 319 [31] Normalintegrale auf offenen Riemannschen Flächen (1947) 320 Commentary 341 [21] OnPhragmen-LindelöPsPrinciple(1937) 342 [25] An Extension of Schwarz's Lemma (1938) 350 Paper 356 [34] (With M. Heins) Questions of regularity connected with the Phragmen- Lindelöfprinciple(1949) 357 Commentary 363 [27] The Theory ofmeromorphiccurves( 1941) 365 Commentary 394 [29] (With A. Beurling) Invariants conformes et problemes extremaux (1946) 395 [35] (With A. Beurling) Conformal invariants and function-theoretic null-sets (1950) 406 [41] (With A. Beurling) Conformal invariants (1952) 435 Commentary 438 [30] Boundedanalyticfunctions(1947) 439 [36] Open Riemann surfaces and extremal problems on compact subregions (1950) 450 Commentary 485 [40] On the characterization ofhyperbolic Riemann surfaces (1952) 486 [42] (With H. L. Royden) A counterexample in the Classification of open Riemann surfaces (1952) 489 vi Lars V. Ahlfors: Collected Papers Volume 1
Paper 492 [43] Development of the theory of conformal mapping and Riemann surfaces through a Century (1953) 493 Commentary 502 [39] Remarks on the Neumann-Poincare integral equation (1952) 503 [46] Two numerical methods in conformal mapping (1955) 513 CONTENTS-Volume 2 About the Organization of These Volumes iv Author's Preface xi Publications of Lars V. Ahlfors xv Commentary 1 [44] On quasiconformal mappings(1954) 2 Commentary 62 [47] Remarks on Riemann surfaces (1955) 63 [48] Square-integrable differentials on open Riemann surfaces (1956) 67 [50] Extremalprobleme in der Funktionentheorie (1958) 70 [51] The method of orthogonal decomposition for differentials on open Riemann surfaces (1958) 77 [52] Abel's theorem for open Riemann surfaces (1958) 90 Commentary 103 [49] (With A. Beurling) The boundary correspondence under quasiconformal mappings (1956) 104 Commentary 122 [54] The complex analytic structure of the space of closed Riemann surfaces (1960) 123 Commentary 145 [55] Classical and contemporary analysis (1961) 146 Commentary 155 [57] Some remarks on Teichmüller's space of Riemann surfaces (1961) 156 [58] Curvature properties of Teichmüller's space (1962) 177 Commentary 193 [59] Geodesic curvature and area( 1962) 194 Commentary 201 [60] (With G. Weil!) A uniqueness theorem for Beltrami equations (1962) 202 Contents VII
Paper 206 [61] Teichmüller Spaces (1963) 207 Commentary 214 [63] Quasiconformal reflections (1963) 215 Commentary 226 [45] Conformality with respect to Riemannian metrics (1955) 227 [53] (With L. Bers) Riemann's mapping theorem for variable metrics (1960) 247 Commentary 267 [64] Extension of quasiconformal mappings from two to three dimensions (1964) 268 Commentary 272 [65] Finitely generated Kleinian groups(1964) 273 [65a] Correction to "Finitely generated Kleinian groups" (1965) 290 Papers 291 [66] Eine Bemerkung über Fuchssche Gruppen (1964) 292 [67] Kleinian groups (1964) 294 [68] Quasiconformal mappings and their applications (1964) 301 Commentary 315 [70] Some remarks on Kleinian groups (1965) 316 [71] Fundamental polyhedrons and limit point sets of Kleinian groups (1966) 320 Paper 324 [72] Remarks on Carleman's formula for functions in a halfplane (1966) 325 Commentary 330 [73] Kleinsche Gruppen in der Ebene und im Raum (1966) 331 [74] Hyperbolicmotions(1967) 340 Commentary 344 [80] Conditions for quasiconformal deformations in several variables (1974) 345 [82] Invariant Operators and integral representations in hyperbolic Space (1975) 352 [89] A singular integral equation connected with quasiconformal mappings in space (1978) 369 Commentary 381 [75] Eichler integrals and the area theorem of Bers (1968) 382 [76] The structure of a finitely generated Kleinian group (1969) 389 [77] Two lectures on Kleinian groups (1971) 406 [78] Remarks on the limit point set of a finitely generated Kleinian group (1971) 422 Commentary 430 [79] Sufficient conditions for quasi-conformal extension (1973) 431 [81] A remark on schlicht functions with quasiconformal extensions (1974) 438 Paper 442 [83] Quasiconformal deformations and mappings inr n (1976) 443 vm Lars V. Ahlfors: Collected Papers Volume 1
Commentary 467 [85] On a class of quasiconformal mappings (1976) 468 [88] A Singular Operator in hyperbolic Space (1977) 474 Commentary 479 [86] An inequality between the coefficients a 3 and a 4 of a Univalent function (1976) 480 Paper 484 [90] Quasiconformal mappings, Teichmüller Spaces, and Kleinian groups (1978) 485 Papers 499 [91] The Holder continuity of quasiconformal deformations (1979) 500 [92] Ergodic properties of groups Möbius transformations (1979) 509 Contents ix