A distortion theorem for doubly connected regions
Author:
Milton N. Parnes
Journal:
Proc. Amer. Math. Soc. 26 (1970), 85-91
MSC:
Primary 30.40
DOI:
https://doi.org/10.1090/S0002-9939-1970-0265569-X
MathSciNet review:
0265569
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
- Charles K. Chui and Milton N. Parnes, Measures of $N$-fold symmetry for convex sets, Proc. Amer. Math. Soc. 26 (1970), 480–486. MR 264514, DOI https://doi.org/10.1090/S0002-9939-1970-0264514-0 G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, New York, 1934.
- Hans P. Künzi, Quasikonforme Abbildungen, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 26, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960 (German). MR 0168757
- Moshe Marcus, Transformations of domains in the plane and applications in the theory of functions, Pacific J. Math. 14 (1964), 613–626. MR 165093 M. N. Parnes, Symmetrization and conformal mapping, Dissertation, Wayne State University, Detroit, Mich., 1968.
- G. Pólya and G. Szegö, Isoperimetric Inequalities in Mathematical Physics, Annals of Mathematics Studies, No. 27, Princeton University Press, Princeton, N. J., 1951. MR 0043486
- G. Szegö, On a certain kind of symmetrization and its applications, Ann. Mat. Pura Appl. (4) 40 (1955), 113–119. MR 77664, DOI https://doi.org/10.1007/BF02416526
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30.40
Retrieve articles in all journals with MSC: 30.40
Additional Information
Keywords:
Doubly connected regions,
<IMG WIDTH="18" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$n$">-fold symmetric,
convex sets,
distortion theorem,
extremal problem
Article copyright:
© Copyright 1970
American Mathematical Society