訂正日: 2006/10/20訂正理由: -訂正箇所: 引用文献情報訂正内容: Wrong : 1) E. Calabi, An extension of E. Hopf's maximum principle, Duke Math. J., 25 (1937), 45-56. 2) Q. Chen and Y. L. Xin, A generalized maximum principle and its applications in geometry, Preprint MSRI (1990), to appear in Amer. J. Math.. 3) S. Y. Cheng, Liouville's theorems for harmonic maps, Proc. Sympos. Pure Math., 36 (1980), 91-94. 4) H. I. Choi and A. Treibergs, Gauss maps of space-like constant mean curvature hypersurfaces of Minkowski space, J. Differential Geom., 32 (1990), 775-817. 5) J. Eells and L. Lemaire, A report on harmonic maps, Bull. London Math. Soc., 10 (1978), 1-68. 6) J. Eells and L. Lemaire, Another report on harmonic maps, Bull. London Math. Soc., 20 (1988), 385-524. 7) J. Eells and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86 (1964), 109-160. 8) R. Greene and H. Wu, Function theory on manifolds which possess a pole, Lecture Notes in Math., 699, Springer, 1979. 9) L. Jorge and D. Koutroufiotis, An estimate for the curvature of bounded submanifolds, Amer. J. Math., 103 (1981), 711-725. 10) L. Karp, Differential inequalities on complete Riemannian manifolds and applications, Math. Ann., 272 (1985), 449-459. 11) A. Kasue, Estimates for solutions of Poisson equations and their applications to submanifolds, (ed. K. Kenmotsu), Lecture Notes in Math., 1090, Springer, 1984, pp. 1-14. 12) R. Osserman, On the inequality Δu_??_f(u), Pacific J. Math., 7 (1957), 1641-1647. 13) A. Ratto and M. Rigoli, On the asymptotic behaviour of rotationally symmetric harmonic maps, J. Differential Equations, to appear. 14) R. Redheffer, A classification of solutions of certain nonlinear differential inequalities with applications to theorems of Liouville type, Math. Z., 192 (1986), 453-465. 15) R. Redheffer, On the inequality Δu_??_f (u, |grad u|), J. Math. Anal. Appl., 1 (1960), 277-299. 16) A. Tachikawa, A non-existence result for harmonic mappings from Rn to Hn, Tokyo J. Math., 11 (1988), 311-316. 17) A. Tachikawa, Harmonic mappings from Rn into an Hadamard manifold, J. Math. Soc. Japan, 42 (1990), 147-153. 18) S. T. Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math., 28 (1975), 201-228.
Right : [1] E. Calabi, An extension of E. Hopf's maximum principle, Duke Math. J., 25 (1957), 45-56. [2] Q. Chen and Y. L. Xin, A generalized maximum principle and its applications in geometry, Preprint MSRI (1990), to appear in Amer. J. Math.. [3] S. Y. Cheng, Liouville's theorems for harmonic maps, Proc. Sympos. Pure Math., 36 (1980), 91-94. [4] H. I. Choi and A. Treibergs, Gauss maps of space-like constant mean curvature hypersurfaces of Minkowski space, J. Differential Geom., 32 (1990), 775-817. [5] J. Eells and L. Lemaire, A report on harmonic maps, Bull. London Math. Soc., 10 (1978), 1-68. [6] J. Eells and L. Lemaire, Another report on harmonic maps, Bull. London Math. Soc., 20 (1988), 385-524. [7] J. Eells and J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math., 86 (1964), 109-160. [8] R. Greene and H. Wu, Function theory on manifolds which possess a pole, Lecture Notes in Math., 699, Springer, 1979. [9] L. Jorge and D. Koutroufiotis, An estimate for the curvature of bounded submanifolds, Amer. J. Math., 103 (1981), 711-725. [10] L. Karp, Differential inequalities on complete Riemannian manifolds and applications, Math. Ann., 272 (1985), 449-459. [11] A. Kasue, Estimates for solutions of Poisson equations and their applications to submanifolds, (ed. K. Kenmotsu), Lecture Notes in Math., 1090, Springer, 1984, pp. 1-14. [12] R. Osserman, On the inequality Δu≥f(u), Pacific J. Math., 7 (1957), 1641-1647. [13] A. Ratto and M. Rigoli, On the asymptotic behaviour of rotationally symmetric harmonic maps, J. Differential Equations, to appear. [14] R. Redheffer, A classification of solutions of certain nonlinear differential inequalities with applications to theorems of Liouville type, Math. Z., 192 (1986), 453-465. [15] R. Redheffer, On the inequality Δu≥f (u, |grad u|), J. Math. Anal. Appl., 1 (1960), 277-299. [16] A. Tachikawa, A non-existence result for harmonic mappings from Rn to Hn, Tokyo J. Math., 11 (1988), 311-316. [17] A. Tachikawa, Harmonic mappings from Rn into an Hadamard manifold, J. Math. Soc. Japan, 42 (1990), 147-153. [18] S. T. Yau, Harmonic functions on complete Riemannian manifolds, Comm. Pure Appl. Math., 28 (1975), 201-228.