Anderson, M. T. The Dirichlet problem at infinity for manifolds of negative curvature. (English) Zbl 0541.53036 J. Differ. Geom. 18, 701-722 (1983). Let \(N^ n\) be a simply connected Riemannian manifold with sectional curvature bounded between two negative constants. The author solves the Dirichlet problem at infinity for \(N^ n\), i.e., given a continuous function on the sphere at infinity \(S^{n-1}(\infty)\), there is a continuous harmonic extension to \(\bar N^ n=N^ n\cup S^{n- 1}(\infty)\). As a consequence it follows that \(N^ n\) has a large class of bounded harmonic functions. This result was proved independently by D. Sullivan by a different method [see the next review]. Reviewer: G.Thorbergsson Cited in 5 ReviewsCited in 86 Documents MSC: 53C20 Global Riemannian geometry, including pinching 31C05 Harmonic, subharmonic, superharmonic functions on other spaces Keywords:manifolds of negative curvature; Dirichlet problem at infinity; harmonic functions Citations:Zbl 0541.53035; Zbl 0541.53037 PDFBibTeX XMLCite \textit{M. T. Anderson}, J. Differ. Geom. 18, 701--722 (1983; Zbl 0541.53036) Full Text: DOI