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Rough isometry and the asymptotic Dirichlet problem. (English) Zbl 0928.58030

The paper proposes a new asymptotic Dirichlet problem for harmonic functions via the rough isometry on a certain class of Riemannian manifolds. The authors define a suitable class of functions \({\mathcal F}_\varphi\) such that the Dirichlet problem is solvable for this class. The main theorem is a generalization of a result due to Schoen and Yau.

MSC:

58J32 Boundary value problems on manifolds
31C05 Harmonic, subharmonic, superharmonic functions on other spaces
31C20 Discrete potential theory
58J05 Elliptic equations on manifolds, general theory
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