Uniqueness of harmonic mappings with Blaschke dilatations |
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| Authors: | D Bshouty A Lyzzaik A Weitsman |
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| Institution: | (1) Department of Mathematics, Technion, 32000 Haifa, Israel;(2) Department of Mathematics, American University of Beirut, Beirut, Lebanon;(3) Department of Mathematics, Purdue University, 47907-1395 West Lafayette, IN |
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| Abstract: | Let Ω be a bounded convex domain and let ω be a finite Blaschke product of order N = 1, 2, .... It is known that the elliptic
differential equation
admits a one-to-one solution normalized by ƒ(0) = 0, ƒz(0) > 0 and maps the open unit disc
onto a convex (n + 2)-gon whose vertices belong to ∂Ω. In this article it is shown that this solution is unique. |
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| Keywords: | Math Subject Classifications" target="_blank">Math Subject Classifications 26C10 30C15 |
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