Collected Papers Vol 2: 1954-1979

When first confronted with the prospect of having my collected papers published, I felt both awe and confusion, but I calmed down when I realized that the purpose was not to honor the author, but to be of service to the mathematical community. If young scholars of a future generation should desire to find out what some mathematicians of the twentieth century were up to, they would indeed have reason to be thankful if spared the need to seek this information from a multi tude of sources. As an introduction it seems polite and useful to begin with a brief outline of my life, especially as related to my professional activity. I was born the eighteenth of April 1907 in Helsingfors, Finland. My father was a professor of mechanical engineering at the Poly technical Institute. My mother died in childbirth when I was born. At the time of my early childhood Finland was under Russian sovereignty, but with a certain degree of autonomy, sometimes observed and sometimes disregarded by the czar who was, by today's standards, a relatively benevolent despot. Civil servants, including professors, were able to enjoy a fairly high standard of living, a condition that was to change radically during World War I and the Russian revolution that followed.

Contenu
Contents-Volume 2.- Commentary.- [44] On quasiconformal mappings (1954).- Commentary.- [47] Remarks on Riemann surfaces (1955).- [48] Square-integrable differentials on open Riemann surfaces (1956).- [50] Extremalprobleme in der Funktionentheorie (1958).- [51] The method of orthogonal decomposition for differentials on open Riemann surfaces (1958).- [52] Abel's theorem for open Riemann surfaces (1958).- Commentary.- [49] (With A. Beurling) The boundary correspondence under quasiconformal mappings (1956).- Commentary.- [54] The complex analytic structure of the space of closed Riemann surfaces (1960).- Commentary.- [55] Classical and contemporary analysis (1961).- Commentary.- [57] Some remarks on Teichmüller's space of Riemann surfaces (1961).- [58] Curvature properties of Teichmüller's space (1962).- Commentary.- [59] Geodesic curvature and area (1962).- Commentary.- [60] (With G. Weill) A uniqueness theorem for Beltrami equations (1962).- Paper.- [61] Teichmüller spaces (1963).- Commentary.- [63] Quasiconformal reflections (1963).- Commentary.- [45] Conformality with respect to Riemannian metrics (1955).- [53] (With L. Bers) Riemann's mapping theorem for variable metrics (1960).- Commentary.- [64] Extension of quasiconformal mappings from two to three dimensions (1964).- Commentary.- [65] Finitely generated Kleinian groups (1964).- [65a] Correction to Finitely generated Kleinian groups (1965).- Papers.- [66] Eine Bemerkung über Fuchssche Gruppen (1964).- [67] Kleinian groups (1964).- [68] Quasiconformal mappings and their applications (1964).- Commentary.- [70] Some remarks on Kleinian groups (1965).- [71] Fundamental polyhedrons and limit point sets of Kleinian groups (1966).- Paper.- [72] Remarks on Carleman's formula for functions in a halfplane(1966).- Commentary.- [73] Kleinsche Gruppen in der Ebene und im Raum (1966).- [74] Hyperbolic motions (1967).- Commentary.- [80] Conditions for quasiconformal deformations in several variables (1974).- [82] Invariant operators and integral representations in hyperbolic space (1975).- [89] A singular integral equation connected with quasiconformal mappings in space (1978).- Commentary.- [75] Eichler integrals and the area theorem of Bers (1968).- [76] The structure of a finitely generated Kleinian group (1969).- [77] Two lectures on Kleinian groups (1971).- [78] Remarks on the limit point set of a finitely generated Kleinian group (1971).- Commentary.- [79] Sufficient conditions for quasi-conformal extension (1973).- [81] A remark on schlicht functions with quasiconformal extensions (1974).- Paper.- [83] Quasiconformal deformations and mappings in Rn (1976).- Commentary.- [85] On a class of quasiconformal mappings (1976).- [88] A singular operator in hyperbolic space (1977).- Commentary.- [86] An inequality between the coefficients a3 and a4of a univalent function (1976).- Paper.- [90] Quasiconformal mappings, Teichmüller spaces, and Kleinian groups (1978).- Papers.- [91] The Holder continuity of quasiconformal deformations (1979).- [92] Ergodic properties of groups Möbius transformations (1979).