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The existence of bounded harmonic functions on C-H manifolds. (English) Zbl 0885.53036
Let \(M\) be a simply connected complete Riemannian manifold with sectional curvatures \(-b^2\leq K_M (\sigma) \leq- A/r^2\), where \(r\) is the distance of the footpoint of \(\sigma\) to a fixed origin of \(M\) and where \(A>4\). The authors show that under these assumptions the Dirichlet problem at infinity can be solved.
Reviewer: W.Ballmann (Bonn)

MSC:
53C20 Global Riemannian geometry, including pinching
31C05 Harmonic, subharmonic, superharmonic functions on other spaces
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References:
[1] Chen, Chinese Sci. Bull. 9 pp 655– (1989)
[2] Ballmann, Form. Math. 1 pp 201– (1990)
[3] DOI: 10.2307/1971181 · Zbl 0587.53045 · doi:10.2307/1971181
[4] Anderson, J. Differential Geom. 18 pp 701– (1983)
[5] Ding, Differential geometry pp 49– (1993)
[6] DOI: 10.1512/iumj.1976.25.25051 · Zbl 0335.53041 · doi:10.1512/iumj.1976.25.25051
[7] Sullivan, J. Differential Geom. 18 pp 723– (1983)
[8] DOI: 10.2307/2318308 · Zbl 0356.53002 · doi:10.2307/2318308
[9] Greene, Function theory on manifolds which possess a pole 699 (1979) · Zbl 0414.53043 · doi:10.1007/BFb0063413
[10] DOI: 10.1002/cpa.3160280203 · Zbl 0291.31002 · doi:10.1002/cpa.3160280203
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