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The existence of bounded harmonic functions on C-H manifolds
Published online by Cambridge University Press: 17 April 2009
Abstract
Let M be a Cartan-Hadamard manifold of dimension n (n ≥ 2). Suppose that M satisfies for every x > M outside a compact set an inequality:
where b, A are positive constants and A > 4. Then M admits a wealth of bounded harmonic functions, more precisely, the Dirichlet problem of the Laplacian of M at infinity can be solved for any continuous boundary data on Sn−1(∞).
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- Copyright © Australian Mathematical Society 1996
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