Diameter problems for univalent functions with quasiconformal extension
This paper utilizes the method of extremal length to study several diameter problems for functions conformal outside of a disc centered at the origin, with a standard normalization, which possess a quasiconformal extension to a ring subdomain of this disc. Known results on the diameter of a compleme...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000857 |
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| _version_ | 1832562683762704384 |
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| author | Paul Deiermann |
| author_facet | Paul Deiermann |
| author_sort | Paul Deiermann |
| collection | DOAJ |
| description | This paper utilizes the method of extremal length to study several diameter problems
for functions conformal outside of a disc centered at the origin, with a standard normalization,
which possess a quasiconformal extension to a ring subdomain of this disc. Known results on the
diameter of a complementary component of the image domain of a univalent function are extended.
Applications to the transfinite diameters of families of non-overlapping functions and an extension
of the Koebe one-quarter theorem are included. |
| format | Article |
| id | doaj-art-94092d1f396e4ae291b3637f7b4b45d3 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-94092d1f396e4ae291b3637f7b4b45d32025-02-03T01:22:09ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116467968610.1155/S0161171293000857Diameter problems for univalent functions with quasiconformal extensionPaul Deiermann0Department of Mathematics, Louisiana State University in Shreveport, Shreveport, Louisiana 71115, USAThis paper utilizes the method of extremal length to study several diameter problems for functions conformal outside of a disc centered at the origin, with a standard normalization, which possess a quasiconformal extension to a ring subdomain of this disc. Known results on the diameter of a complementary component of the image domain of a univalent function are extended. Applications to the transfinite diameters of families of non-overlapping functions and an extension of the Koebe one-quarter theorem are included.http://dx.doi.org/10.1155/S0161171293000857extremal problemsunivalent functionsquasiconformal extensions diameter theorems. |
| spellingShingle | Paul Deiermann Diameter problems for univalent functions with quasiconformal extension International Journal of Mathematics and Mathematical Sciences extremal problems univalent functions quasiconformal extensions diameter theorems. |
| title | Diameter problems for univalent functions with quasiconformal extension |
| title_full | Diameter problems for univalent functions with quasiconformal extension |
| title_fullStr | Diameter problems for univalent functions with quasiconformal extension |
| title_full_unstemmed | Diameter problems for univalent functions with quasiconformal extension |
| title_short | Diameter problems for univalent functions with quasiconformal extension |
| title_sort | diameter problems for univalent functions with quasiconformal extension |
| topic | extremal problems univalent functions quasiconformal extensions diameter theorems. |
| url | http://dx.doi.org/10.1155/S0161171293000857 |
| work_keys_str_mv | AT pauldeiermann diameterproblemsforunivalentfunctionswithquasiconformalextension |