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The existence of bounded harmonic functions on C-H manifolds

Published online by Cambridge University Press:  17 April 2009

Qing Ding  and
Detang Zhou
Qing Ding
Affiliation:
Institute of MathematicsFudan UniversityShanghai 200433China
Detang Zhou
Affiliation:
Department of MathematicsShandong UniversityJinan, Shandong 250100China
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Abstract

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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(∞).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 2 , April 1996 , pp. 197 - 207
Copyright
Copyright © Australian Mathematical Society 1996

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