Ricci curvature, geodesics and some geometric properties of Riemannian manifolds with boundary

Atsushi KASUE

doi:10.2969/jmsj/03510117

Atsushi KASUE

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JOURNAL FREE ACCESS

1983 Volume 35 Issue 1 Pages 117-131

DOI https://doi.org/10.2969/jmsj/03510117

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Published: 1983 Received: September 14, 1981 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc., 145 (1969), 1-49.
2) E. Bombieri, E. de Giorgi and E. Giusti, Minimal cones and the Bernstein problem, Invent. Math., 7 (1969), 243-268.
3) Yu. D. Burago and V.A. Zalgaller, Convex sets in Riemannian spaces of non-negative curvature, Uspehi Mat. Nauk, 32 (1977), 3-55; Russian Math. Surveys, 32 (1977), 1-57.
4) J. Cheeger and D. Gromoll, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Differential Geometry, 6 (1971), 119-128.
5) J. Cheeger and D. Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math., 96 (1972), 413-443.
6) S.-Y. Cheng, Eigenvalue comparison theorems and its geometric applications, Math. Z., 143 (1975), 289-297.
7) E. Heintze and H. Karcher, A general comparison theorem with applications to volume estimates for submanifolds, Ann. Sci. École Norm. Sup., 11 (1978), 451-470.
8) R. Ichida, Riemannian manifolds with compact boundary, Yokohama Math. J., 29 (1981), 169-177.
9) A. Kasue, A Laplacian comparison theorem and function theoretic properties of a complete Riemannian manifold, to appear in Japan. J. Math., 8 (1982).
10) S. Sternberg, Lectures on differential geometry, Prentice-Hall, Inc., New Jersey, 1965.
11) H. Wu, An elementary method in the study of nonnegative curvature, Acta Math., 142 (1979), 57-78.

Right : [1] R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc., 145 (1969), 1-49.
[2] E. Bombieri, E. de Giorgi and E. Giusti, Minimal cones and the Bernstein problem, Invent. Math., 7 (1969), 243-268.
[3] Yu. D. Burago and V.A. Zalgaller, Convex sets in Riemannian spaces of non-negative curvature, Uspehi Mat. Nauk, 32 (1977), 3-55; Russian Math. Surveys, 32 (1977), 1-57.
[4] J. Cheeger and D. Gromoll, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Differential Geometry, 6 (1971), 119-128.
[5] J. Cheeger and D. Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math., 96 (1972), 413-443.
[6] S. -Y. Cheng, Eigenvalue comparison theorems and its geometric applications, Math. Z., 143 (1975), 289-297.
[7] E. Heintze and H. Karcher, A general comparison theorem with applications to volume estimates for submanifolds, Ann. Sci. École Norm. Sup., 11 (1978), 451-470.
[8] R. Ichida, Riemannian manifolds with compact boundary, Yokohama Math. J., 29 (1981), 169-177.
[9] A. Kasue, A Laplacian comparison theorem and function theoretic properties of a complete Riemannian manifold, to appear in Japan. J. Math., 8 (1982).
[10] S. Sternberg, Lectures on differential geometry, Prentice-Hall, Inc., New Jersey, 1965.
[11] H. Wu, An elementary method in the study of nonnegative curvature, Acta Math., 142 (1979), 57-78.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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