The Dirichlet problem at infinity on Hadamard manifolds
Source: Nagoya Math. J. Volume 138 (1995), 1-18.
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 K. Akutagawa, The Dirichlet problem at infinity for harmonic mapping between Hadamard manifolds, Geometry of Manifolds, ed.by K. Shiohama, Academic Press, 1989, 59-70.
 A. Ancona, Negatively curved manifolds, elliptic operators, andthe Martin bound- ary, Ann.of Math., 125(1987), 495-536.
 M. T. Anderson, The Dirichlet problem at infinity for manifolds of negative curva- ture, J. Differential Geom., 18 (1983), 701-721.
 M, T. Anderson and R. Schoen, Positive harmonic functions on complete manifolds of negative curvature, Ann. of Math., 121 (1985), 429-461.
 P. Aviles, H. I. Choi and M. Micallef, Boundary behavior of Harmonic maps on negatively curved manifolds, J. Funct. Anal., 99 (1991), 293-331.
 R. Azencott, Behavior of diffusion semigroups at infinity, Bulletin Soc. Math. France, 102 (1974), 193-240.
 W. Ballmann, On the Dirichlet problem at infinity of manifolds of nonpositive curv- ature, Forum Math., 1 (1989), 201-213.
 S. Y. Cheng, The Dirichlet problem at infinity for nonpositively curved manifolds, Communications in Analysis and Geometry, 1 (1993), 101 – 112.
Mathematical Reviews (MathSciNet): MR1230275
 H. I. Choi, Asymptotic Dirichlet problems for Harmonic functions on Riemannian manifolds, Trans, of Amer. Math. Soc, 281, 2, Feb., 1984.
 J. Dodziuk, Maximum principle for parabolic inequalities and the heat flow on open manifolds, Indiana Univ. Math.J., 32 (1983), 703-716.
 P. Eberlein and B. O'Neill, Visibility manifolds, Pacific J. Math., 46 (1973), 45-109.
 J. Eells and L. Lemaire, Selected topics in harmonic maps, C.B.M.S. Regional Conf. Series 50 (Amer. Math. Soc, Providence, R. I. 1983).
 J. Eelles and Lamaire, Another report on harmonic maps, Bull. London Math. Soc, 20(1988), 385-524.
 P. Hsu, Brownian motion and Riemannian geometry, Contemp. Math. 73 (1988), 95-104.
 P. Hsu and P. March, The Limiting angle of certain Riemannian Brownian motions, Comm. on Pure Appl. Math.,38 (1985), 755-768.
 A. Kasue, Applications of Laplacian and Hessian comparison theorems, Advanced Studies in Pure Mathematics 3, Kinokuniya, Tokyo.
 A. Kasue, Harmonic functions of polynomial growth on complete manifolds, Pro- ceeding of Symposia in Pure Mathematics, 54 (1993), Part 1.
 P. Li and S. T. Yau, On the parabolic kernel of the Schrdinger operator, Acta Math., 156 (1986), 153-201.
 M. Murata, Uniqueness and non-uniqueness of the positive Cauchy problem for the heat equation on Riemannian manifolds, preprint.
 T. Sasaki, On the Green function of a complete Riemannian or Kahlar manifold with asymptotically negative constant curvature and applications, Advanced Stu- dies in Pure Mathematics 3, Kinokuniya, Tokyo.
 D. Sullivan, The Dirichlet problem at infinity for a negatively curved manifold, J. Differential Geom., 18 (1983), 723-732.