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Conformal Geometry and Dynamics

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A uniqueness theorem for harmonic functions on the upper-half plane


Author: Biao Ou
Journal: Conform. Geom. Dyn. 4 (2000), 120-125
MSC (2000): Primary 53A30, 35J05, 30C15
DOI: https://doi.org/10.1090/S1088-4173-00-00067-9
Published electronically: December 15, 2000
MathSciNet review: 1799653
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Abstract: Consider harmonic functions on the upper-half plane $R^{2}_{+}\! = \{(x,y)|\;y > 0 \}$ satisfying the boundary condition $u_{y}=-\exp (u)$ and the constraint $\int _{R^{2}_{+}}\exp (2u) < \infty$. We prove that all such functions are of form (1.2) below.


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Additional Information

Biao Ou
Affiliation: Department of Mathematics, University of Toledo, Toledo, Ohio 43606
Email: bou@math.utoledo.edu

Keywords: Harmonic, analytic, the Picard theorems
Received by editor(s): August 14, 2000
Published electronically: December 15, 2000
Article copyright: © Copyright 2000 American Mathematical Society