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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Quasiconformal variation of slit domains
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by Clifford J. Earle and Adam Lawrence Epstein PDF
Proc. Amer. Math. Soc. 129 (2001), 3363-3372 Request permission

Abstract:

We use quasiconformal variations to study Riemann mappings onto variable single slit domains when the slit is the tail of an appropriately smooth Jordan arc. In the real analytic case our results answer a question of Dieter Gaier and show that the function $\kappa$ in Löwner’s differential equation is real analytic.
References
  • Saunders MacLane, Steinitz field towers for modular fields, Trans. Amer. Math. Soc. 46 (1939), 23–45. MR 17, DOI 10.1090/S0002-9947-1939-0000017-3
  • Lars V. Ahlfors, Conformal invariants: topics in geometric function theory, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. MR 0357743
  • Lars Ahlfors and Lipman Bers, Riemann’s mapping theorem for variable metrics, Ann. of Math. (2) 72 (1960), 385–404. MR 115006, DOI 10.2307/1970141
  • L. Brickman, Y. J. Leung, and D. R. Wilken, On extreme points and support points of the class $S$, Ann. Univ. Mariae Curie-Skłodowska Sect. A 36/37 (1982/83), 25–31 (1985) (English, with Russian and Polish summaries). MR 808430
  • Soo Bong Chae, Holomorphy and calculus in normed spaces, Monographs and Textbooks in Pure and Applied Mathematics, vol. 92, Marcel Dekker, Inc., New York, 1985. With an appendix by Angus E. Taylor. MR 788158
  • Peter L. Duren, Univalent functions, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 259, Springer-Verlag, New York, 1983. MR 708494
  • C. J. Earle and S. Mitra, Variation of moduli under holomorphic motions, Contemp. Math. 256, Amer. Math. Soc., Providence, RI, 2000.
  • P. Hebroni, Sur les inverses des éléments dérivables dans un anneau abstrait, C. R. Acad. Sci. Paris 209 (1939), 285–287 (French). MR 14
  • Leonard Eugene Dickson, New First Course in the Theory of Equations, John Wiley & Sons, Inc., New York, 1939. MR 0000002
  • D. Marshall and S. Rohde, The Löwner differential equation and slit discs, in preparation.
  • Ch. Pommerenke, Boundary behaviour of conformal maps, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 299, Springer-Verlag, Berlin, 1992. MR 1217706, DOI 10.1007/978-3-662-02770-7
  • Burton Rodin, Behavior of the Riemann mapping function under complex analytic deformations of the domain, Complex Variables Theory Appl. 5 (1986), no. 2-4, 189–195. MR 846487, DOI 10.1080/17476938608814139
  • H. L. Royden, Löwner’s kappa function when the slit is analytic, with applications, M. S. Thesis, Stanford University, 1949.
  • P. Erdös and T. Grünwald, On polynomials with only real roots, Ann. of Math. (2) 40 (1939), 537–548. MR 7, DOI 10.2307/1968938
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Additional Information
  • Clifford J. Earle
  • Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
  • Email: cliff@math.cornell.edu
  • Adam Lawrence Epstein
  • Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
  • Address at time of publication: Department of Mathematics, University of Warwick, Coventry CV4 7AL, England
  • Email: adame@math.cornell.edu, adame@maths.warwick.ac.uk
  • Received by editor(s): January 27, 2000
  • Received by editor(s) in revised form: March 24, 2000
  • Published electronically: January 29, 2001
  • Additional Notes: The second author was supported in part by NSF Grant DMS 9803242.
  • Communicated by: Albert Baernstein II
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 3363-3372
  • MSC (2000): Primary 30C20, 30C62
  • DOI: https://doi.org/10.1090/S0002-9939-01-05991-3
  • MathSciNet review: 1845014