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A note on the Dirichlet problem at infinity for manifolds of negative curvature


Author: Albert Borbély
Journal: Proc. Amer. Math. Soc. 114 (1992), 865-872
MSC: Primary 58G20; Secondary 53C20, 58G30
DOI: https://doi.org/10.1090/S0002-9939-1992-1069289-8
MathSciNet review: 1069289
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Abstract: M. T. Anderson and D. Sullivan showed that the Dirichlet problem at infinity for simply connected manifolds is solvable if the curvature satisfies $ - {a^2} < K < - {b^2}$. Using M. T. Anderson's method we generalize this statement to manifolds satisfying the weaker bounds $ - g(r) < K < - {b^2}$, where $ g(r) \approx {e^{\lambda r}}$, with $ \lambda < 1/3$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1069289-8
Keywords: Dirichlet problem, harmonic functions
Article copyright: © Copyright 1992 American Mathematical Society

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