Asymptotic Dirichlet problems for harmonic functions on Riemannian manifolds

Choi, Hyeong In

doi:10.1090/S0002-9947-1984-0722769-4

Asymptotic Dirichlet problems for harmonic functions on Riemannian manifolds
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Trans. Amer. Math. Soc. 281 (1984), 691-716 Request permission

Abstract:

We define the asymptotic Dirichlet problem and give a sufficient condition for solving it. This proves an existence of nontrivial bounded harmonic functions on certain classes of noncompact complete Riemannian manifolds.

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