zbMATH — the first resource for mathematics

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)

53C20 Global Riemannian geometry, including pinching
31C05 Harmonic, subharmonic, superharmonic functions on other spaces
Full Text: DOI
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.