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Proceedings of the American Mathematical Society

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A distortion theorem for doubly connected regions

Author: Milton N. Parnes
Journal: Proc. Amer. Math. Soc. 26 (1970), 85-91
MSC: Primary 30.40
MathSciNet review: 0265569
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Abstract: In this paper we use a symmetrization result of Szegö and a geometric lemma to generalize a distortion theorem of Pólya and Szegö for simply connected regions to doubly connected regions.

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  • [1] C. K. Chui and M. N. Parnes, Measures of $ N$-fold symmetry for convex sets, Proc. Amer. Math. Soc. (to appear). MR 0264514 (41:9107)
  • [2] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, New York, 1934.
  • [3] H. P. Künzi, Quasikonforme Abbildungen, Ergebnisse der Mathematik und ihrer Grenzgebiete, Heft 26, Springer-Verlag, Berlin, 1960. MR 29 #6013. MR 0168757 (29:6013)
  • [4] M. Marcus, Transformations of domains in the plane and applications in the theory of functions, Pacific J. Math. 14 (1964), 613-626. MR 29 #2382. MR 0165093 (29:2382)
  • [5] M. N. Parnes, Symmetrization and conformal mapping, Dissertation, Wayne State University, Detroit, Mich., 1968.
  • [6] G. Pólya and G. Szegö, Isoperimetric inequalities in mathematical physics, Ann. of Math. Studies, no. 27, Princeton Univ. Press, Princeton, N. J., 1951. MR 13, 270. MR 0043486 (13:270d)
  • [7] G. Szegö, On a certain kind of symmetrization and its applications, Ann. Mat. Pura Appl. (4) 40 (1955), 113-119. MR 17, 1074. MR 0077664 (17:1074b)

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Keywords: Doubly connected regions, $ n$-fold symmetric, convex sets, distortion theorem, extremal problem
Article copyright: © Copyright 1970 American Mathematical Society

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