Lars Ahlfors | Academic Influence

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Lars Ahlfors

Mathematics

#62

World Rank

#187

Historical Rank

Measure Theory

#201

World Rank

#312

Historical Rank

mathematics Degrees

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Mathematics

Lars Ahlfors's Degrees

PhD Mathematics University of Helsinki

Why Is Lars Ahlfors Influential?

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According to Wikipedia, Lars Valerian Ahlfors was a Finnish mathematician, remembered for his work in the field of Riemann surfaces and his textbook on complex analysis. Background Ahlfors was born in Helsinki, Finland. His mother, Sievä Helander, died at his birth. His father, Axel Ahlfors, was a professor of engineering at the Helsinki University of Technology. The Ahlfors family was Swedish-speaking, so he first attended the private school Nya svenska samskolan where all classes were taught in Swedish. Ahlfors studied at University of Helsinki from 1924, graduating in 1928 having studied under Ernst Lindelöf and Rolf Nevanlinna. He assisted Nevanlinna in 1929 with his work on Denjoy's conjecture on the number of asymptotic values of an entire function. In 1929 Ahlfors published the first proof of this conjecture, now known as the Denjoy–Carleman–Ahlfors theorem. It states that the number of asymptotic values approached by an entire function of order ρ along curves in the complex plane going toward infinity is less than or equal to 2ρ.

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Lars Ahlfors's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Complex Analysis (1979) (1933)
Lectures on quasiconformal mappings (1966) (999)
Conformal Invariants: Topics in Geometric Function Theory (1973) (997)
RIEMANN'S MAPPING THEOREM FOR VARIABLE METRICS* (1960) (601)
Conformal invariants and function-theoretic null-sets (1950) (429)
The boundary correspondence under quasiconformal mappings (1956) (428)
Contributions to analysis : a collection of papers dedicated to Lipman Bers (1974) (367)
On quasiconformal mappings (1953) (364)
An extension of Schwarz’s lemma (1938) (350)
Complex analysis : an introduction to the theory of analytic functions of one complex variable / Lars V. Ahlfors (1953) (285)
Some Remarks on Teichmuller's Space of Riemann Surfaces (1961) (265)
Finitely Generated Kleinian Groups (1964) (253)
An introduction to the theory of analytic functions of one complex variable (1978) (225)
Möbius transformations in several dimensions (1981) (207)
A uniqueness theorem for Beltrami equations (1962) (187)
Zur Theorie der Überlagerungsflächen (1935) (180)
The theory of meromorphic curves (1941) (158)
Quasiconformal reflections (1963) (126)
Open Riemann surfaces and extremal problems on compact subregions (1950) (121)
Bounded analytic functions (1947) (115)
Möbius transformations in expressed through 2×2 matrices of clifford numbers (1986) (115)
The Complex Analytic Structure of the Space of Closed Riemann Surfaces (1960) (107)
Möbius Transformations and Clifford Numbers (1985) (97)
Curvature properties of Teichmüller’s space (1961) (82)
Fundamental polyhedrons and limit point sets of kleinian groups. (1966) (77)
Questions of regularity connected with the Phragmen-Lindelof principle (1949) (70)
Quasiconformal deformations and mappings inRn (1976) (66)
Remarks on the Neumann-Poincaré integral equation (1952) (65)
On the fixed points of Möbius transformations in R^n (1985) (59)
Über die Blochsche Konstante (1937) (52)
Cross-ratios and Schwarzian Derivatives in Rn (1988) (51)
Untersuchungen zur Theorie der Konformen Abbildung und der Ganzen Funktionen (1982) (49)
Old and new in Möbius groups (1984) (43)
Chapter II. Riemann Surfaces (1960) (38)
The structure of a finitely generated Kleinian group (1969) (37)
Clifford Numbers and Möbius Transformations in Rn (1986) (36)
On the Mathematics Curriculum of the High School (1962) (35)
Sufficient Conditions for Quasi-Conformal Extension (1974) (35)
EXTENSION OF QUASICONFORMAL MAPPINGS FROM TWO TO THREE DIMENSIONS. (1964) (34)
WITH VALUES IN A BANACH SPACE (1988) (33)
Conformality with Respect to Riemannian Metrics (1982) (32)
On Phragmén-Lindelöf’s principle (1937) (31)
Über eine in der neueren Wertverteilungstheorie betrachtete Klasse transzendenter Funktionen. (1932) (25)
Conditions for Quasiconformal Deformations in Several Variables (1974) (23)
Invariant operators and integral representations in hyperbolic space. (1975) (22)
Advances in the theory of Riemann surfaces : proceedings of the 1969 Stony Brook Conference (1971) (19)
CORRECTION TO " FINITELY GENERATED KLEINIAN GROUPS." (1965) (18)
Development of the Theory of Conformal Mapping and Riemann Surfaces Through a Century (1953) (18)
Quasiconformal Mappings and Their Applications (1982) (15)
Some remarks on clifford algebras (1989) (14)
Correction to “On quasiconformal mappings” (1953) (14)
Quasiconformal Mappings, Teichmüller Spaces, and Kleinian Groups (1978) (13)
Classical and Contemporary Analysis (1961) (13)
Review: M. M. Schiffer and D. C. Spencer, Functionals of finite Riemann surfaces (1955) (12)
Über Die Asymptotischen Werte der Meromorphen Funktionen Endlicher Ordnung (1982) (12)
Zur Bestimmung des Typus einer Riemannschen Fläche (1931) (11)
Kleinsche Gruppen in der Ebene und im Raum (1966) (11)
A somewhat new approach to quasiconformal mappings in Rn (1977) (10)
Eichler integrals and the area theorem of Bers. (1968) (9)
Ein Satz von Henri Cartan und seine Anwendung auf die Theorie der meromorphen Funktionen (1982) (8)
Das Dirichletsche Prinzip (1947) (8)
Beiträge zur Theorie der meromorphen Funktionen (1982) (8)
Eine Bemerkung über Fuchssche Gruppen (1964) (7)
Über eine Methode in der Theorie der meromorphen Funktionen (1982) (7)
A Remark on Schlicht Functions with Quasiconformal Extensions (1974) (7)
Review: A. C. Schaeffer and D. C. Spencer, Coefficient regions for schlicht functions (1951) (7)
Variational methods in function theory (1953) (6)
Collected Papers Volume 1 1929–1955 (1982) (6)
Quasiconformal Mappings and Teichmüller’s Theorem (1960) (6)
The Modular Function and Geometric Properties of Quasiconformal Mappings (1965) (5)
Collected Papers Volume 2 1954–1979 (1982) (5)
Ueber die Kreise die von einer Riemannschen Fläche schlicht überdeckt werden (1933) (5)
Gesammelte Abhandlungen = Collected papers (1982) (5)
Remarks on Carleman's Formula for Functions in a Half-Plane (1966) (5)
Über die Anwendung Differentialgeometrischer Methoden zur Untersuchung von Überlagerungsflächen (1982) (4)
Some Remarks on Kleinian Groups (1982) (4)
Extremalprobleme in der Funktionentheorie (1982) (3)
Über eine Klasse von Riemannschen Flächen (1982) (3)
Arne Beurling in memoriam (1988) (3)
Normalintegrale Auf Offenen Riemannschen Flächen (1982) (3)
Riemann surfaces and small point sets (1982) (3)
Two Lectures on Kleinian Groups (1982) (3)
THE THEOREM OF RIEMANN-ROCH FOR ADJOINT SYSTEMS ON KÄHLERIAN VARIETIES (1953) (2)
Geodesic Curvature and Area (1982) (2)
Ergodic properties of groups of Möbius transformations (1980) (2)
Hyperbolic Motions (1967) (2)
Remarks on Riemann Surfaces (1982) (2)
Abel’s Theorem for Open Riemann Surfaces (1982) (2)
The story of a friendship: Recollections of Arne Beurling (1993) (2)
Über die asymptotischen Werte der ganzen Funktionen endlicher Ordnung (1982) (2)
Contributions to the Theory of Riemann Surfaces. (AM-30) (1953) (2)
A Singular Integral Equation Connected with Quasiconformal Mappings in Space (1982) (2)
Remarks on the Limit Point Set of a Finitely Generated Kleinian Group (1971) (2)
Rolf Nevanlinna in memoriam (1982) (2)
The Holder Continuity of Quasiconformal Deformations (1979) (2)
Classical analysis: Present and future (1986) (1)
Das mathematische Schaffen Rolf Nevanlinnas (1976) (1)
THE BINOMIAL THEOREM IN THE ALGEBRA A (1991) (1)
Lars Valerian Ahlfors: Collected Papers, Volume I, 1929-1955, Volume II, 1954-1979. (1985) (1)
An Interview with Lars V. Ahlfors (1998) (1)
The method of orthogonal decomposition for differentials on open Riemann surfaces (1982) (1)
Contributions to the theory of Riemann surfaces : centennial celebration of Riemann's dissertation (1953) (1)
Two Numerical Methods in Conformal Mapping (1982) (1)
Advances in the Theory of Riemann Surfaces. (AM-66), Volume 66 (1971) (1)
SQUARE-INTEGRABLE DIFFERENTIALS ON OPEN RIEMANN SURFACES. (1956) (1)
Über die konforme Abbildung von Überlagerungsflächen (1982) (0)
Ein Satz über die charakteristische Funktion und den Maximalmodul einer meromorphen Funktion (1982) (0)
On the characterization of hyperbolic Hiemann surfaces (1982) (0)
Chapter III. Harmonic Functions on Riemann Surfaces (1960) (0)
Chapter I. Surface Topology (1960) (0)
Review: Marston Morse, Topological methods in the theory of functions of a complex variable (1948) (0)
Geometrie der Riemannschen Flächen (1982) (0)
[Group work method and its application in clinical nursing education]. (1974) (0)
Effect of Signal Bandwidth on the Accuracy of Signal Reconstruction from Its Phase (1984) (0)
Cortona Summer Course Notes (2003) (0)
Chapter IV. Classification Theory (1960) (0)
An Inequality between the Coefficients a 3 and a 4 of a Univalent Function (1982) (0)
Chapter V. Differentials on Riemann Surfaces (1960) (0)
[Suffering encountered on the way]. (1977) (0)
Appendix Papers presented in the Seminars (Titles and Authors) (1960) (0)
In troduc t ion One of the fundamental results of the theory of discontinuous groups of fractional linear transformations acting on the complex plane C is the following finiteness theorem of (0)
A Singular Operator in Hyperbolic Space (1982) (0)
Some problems of mathematics and mechanics : on the occasion of the seventieth birthday of Academician M.A. Lavrentʹev (1976) (0)
Commentationes in honorem Ernesti Leonardi Lindelöf, die VII mensis Martii A. MCMXXX sexagenarii (0)
Complex analysis, Joensuu 1987 : proceedings of the XIIIth Rolf Nevanlinna-Colloquium, held in Joensuu, Finland, Aug. 10-13, 1987 (1988) (0)
A Counterexample in the Classification of open Riemann surfaces (1982) (0)
Die Begründung des Dirichletschen Prinzips (1982) (0)
COMMENTARY ON: ZUR THEORIE DER ÜBERLAGERUNGSFLÄCHEN (1935) (1997) (0)

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