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Concentration of area in half-planes |
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| Authors: | Roger W Barnard Clint Richardson Alexander Yu Solynin |
| Institution: | Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409 ; Department of Mathematics and Statistics, Stephen F. Austin State University, Nacogdoches, Texas 75962 ; Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409 |
| Abstract: | For the standard class  of normalized univalent functions  analytic in the unit disk  , we consider a problem on the minimal area of the image  concentrated in any given half-plane. This question is related to a well-known problem posed by A. W. Goodman in 1949 that regards minimizing area covered by analytic univalent functions under certain geometric constraints. An interesting aspect of this problem is the unexpected behavior of the candidates for extremal functions constructed via geometric considerations. |
| Keywords: | Minimal area problem univalent function local variation symmetrization |
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