Volume estimate of submanifolds in compact Riemannian manifolds

Masao MAEDA

doi:10.2969/jmsj/03030533

Masao MAEDA

著者情報

ジャーナルフリー

1978 年 30 巻 3 号 p. 533-551

DOI https://doi.org/10.2969/jmsj/03030533

詳細

Published: 1978 Received: 1977/04/13 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
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) R. L. Bishop and R. J. Crittenden, Geometry of Manifolds, Academic Press, New York, 1964.
2) J. Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math., 92 (1970), 61-74.
3) T. Frankel, On the fundamental group of a compact minimal submanifold, Ann. of Math., 83 (1966), 68-73.
4) D. Gromoll, W. Klingenberg and W. Meyer, Riemannsche Geomerie im Grossen,Springer-Verlag, 1968.
5) N. Grossman, The volume of a totally geodesic hypersurface in a pinched manifold, Paciffic J. Math., 23 (1967), 257-262.
6) N. Grossman, Two applications of the technique of length decreasing variations, Proc. Amer. Math. Soc., 18 (1967), 327-333.
7) C. Heim, Une borne la longueur des géodésiques périodiques d'une variété riemannienecompacte, These, Université Paris, 1971.
8) D. Hoffman and J. Spruck, Sobolev and isoperimetric inequalities for Riemannian submanifolds, Comm. Pure Appl. Math., 27 (1974), 715-727.
9) F. W. Warner, Extension of the Rauch comparison theorem to submanifolds, Trans. Amer. Math. Soc., 122 (1966), 341-356.

Right : [1] R. L. Bishop and R. J. Crittenden, Geometry of Manifolds, Academic Press, New York, 1964.
[2] J. Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math., 92 (1970), 61-74.
[3] T. Frankel, On the fundamental group of a compact minimal submanifold, Ann. of Math., 83 (1966), 68-73.
[4] D. Gromoll, W. Klingenberg and W. Meyer, Riemannsche Geomerie im Grossen,Springer-Verlag, 1968.
[5] N. Grossman, The volume of a totally geodesic hypersurface in a pinched manifold, Paciffic J. Math., 23 (1967), 257-262.
[6] N. Grossman, Two applications of the technique of length decreasing variations, Proc. Amer. Math. Soc., 18 (1967), 327-333.
[7] C. Heim, Une borne la longueur des géodésiques périodiques d'une variété riemanniene compacte, These, Université Paris, 1971.
[8] D. Hoffman and J. Spruck, Sobolev and isoperimetric inequalities for Riemannian submanifolds, Comm. Pure Appl. Math., 27 (1974), 715-727.
[9] F. W. Warner, Extension of the Rauch comparison theorem to submanifolds, Trans. Amer. Math. Soc., 122 (1966), 341-356.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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