A compactification of a manifold with asymptotically nonnegative curvature
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 21 (1988) no. 4, pp. 593-622. 
@article{ASENS_1988_4_21_4_593_0,
     author = {Kasue, Atsushi},
     title = {A compactification of a manifold with asymptotically nonnegative curvature},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {593--622},
     publisher = {Elsevier},
     volume = {Ser. 4, 21},
     number = {4},
     year = {1988},
     doi = {10.24033/asens.1569},
     mrnumber = {90d:53049},
     zbl = {0662.53032},
     language = {en},
     url = {http://archive.numdam.org/articles/10.24033/asens.1569/}
}
TY  - JOUR
AU  - Kasue, Atsushi
TI  - A compactification of a manifold with asymptotically nonnegative curvature
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1988
SP  - 593
EP  - 622
VL  - 21
IS  - 4
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.24033/asens.1569/
DO  - 10.24033/asens.1569
LA  - en
ID  - ASENS_1988_4_21_4_593_0
ER  - 
%0 Journal Article
%A Kasue, Atsushi
%T A compactification of a manifold with asymptotically nonnegative curvature
%J Annales scientifiques de l'École Normale Supérieure
%D 1988
%P 593-622
%V 21
%N 4
%I Elsevier
%U http://archive.numdam.org/articles/10.24033/asens.1569/
%R 10.24033/asens.1569
%G en
%F ASENS_1988_4_21_4_593_0
Kasue, Atsushi. A compactification of a manifold with asymptotically nonnegative curvature. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 21 (1988) no. 4, pp. 593-622. doi : 10.24033/asens.1569. http://archive.numdam.org/articles/10.24033/asens.1569/

[1] U. Abresch, Lower Curvature Bounds, Toponogov's Theorem, and Bounded Topology (Ann. scient. Éc. Norm. Sup., Paris, Vol. 28, 1985, pp. 651-670). | Numdam | MR | Zbl

[2] M. T. Anderson, The Compactification of a Minimal Submanifold in Euclidean Space by the Gauss Map, preprint.

[3] W. Ballmann, M. Gromov and V. Schroeder, Manifolds of Nonpositive Curvature (Progress in Math., No. 61, Birkhöuser, Boston-Basel-Stuttgart, 1985). | MR | Zbl

[4] J. Cheeger and D. C. Ebin, Comparison Theorems in Riemannian Geometry, North-Holland Math., Libraly 9, North-Holland Publ. Amsterdam-Oxford-New York, 1975. | MR | Zbl

[5] J. Cheeger and D. Gromoll, The Splitting Theorem for Manifolds of Nonnegative Ricci Curvature (J. Differential Geom., Vol. 6, 1971, pp. 119-128). | MR | Zbl

[6] J. Cheeger and D. Gromoll, On the Structure of Complete Manifolds of Nonnegative Curvature (Ann. of Math., Vol. 96, 1974, pp. 413-443). | MR | Zbl

[7] S. Y. Cheng, P. Li and S. T. Yau, On the Upper Estimate of the Heat Kernel of a Complete Riemannian Manifold (Amer. J. Math. Vol. 103, 1981, pp. 1021-1063). | MR | Zbl

[8] H. Donnely and P. Li, Heat Equation and Compactification of Complete Riemannian Manifolds (Duke Math. J., Vol. 51, 1984, pp. 667-673). | MR | Zbl

[9] K. Fukaya, On a Compactification of the Set of Riemannian Manifolds with Bounded Curvatures and Diameters, Curvature and Topology of Riemannian Manifolds (Lecture Notes in Math., No. 1201, Springer-Verlag, 1986). | MR | Zbl

[10] R. E. Greene and H. Wu, C∞ Convex Functions and Manifolds of Positive Curvature (Acta Math., Vol. 137, 1976, pp. 209-245). | MR | Zbl

[11] R. E. Greene and H. Wu, Function Theory on Manifolds which Possess a Pole (Lecture Notes in Math., No. 699, Springer-Verlag, 1979). | MR | Zbl

[12] R. E. Greene and H. Wu, C∞ Approximation of Convex, Subharmonic and Plurisubharmonic Functions (Ann. scient. Ec. Norm. Sup., Paris, Vol. 12, 1979, pp. 47-84). | Numdam | MR | Zbl

[13] R. E. Greene and H. Wu, Lipschitz Convergence of Riemannian Manifolds, (Pacific J. Math., Vol. 131, 1988, pp. 119-141). | MR | Zbl

[14] M. Gromov, Curvature, Diameter, and Betti Numbers (Comment. Math. Helv., Vol. 56, 1981, pp. 179-195). | MR | Zbl

[15] M. Gromov, Structures métriques pour les variétés riemanniennes, redigé par J. LAFONTAINE et P. PANSU, Textes Math., No. 1, Edic/Fernand Nathan, Paris, 1981. | MR | Zbl

[16] K. Grove and K. Shiohama, A Generalized Sphere Theorem (Ann. of Math., Vol. 106, 1977, pp. 201-211). | MR | Zbl

[17] A. Kasue, A Laplacian Comparison Theorem and Function Theoretic Properties of a Complete Riemannian Manifold (Japan. J. Math., Vol. 8, 1982, pp. 309-341). | MR | Zbl

[18] A. Kasue, Applications of Laplacian and Hessian Comparison Theorems, Geometry of Geodesics and Related Topics, K. SHIOHAMA Ed., Advanced Studies in Pure Math., Vol. 3, 1984, pp. 333-386. | MR | Zbl

[19] A. Kasue, On Manifolds of Asymptotically Nonnegative Curvature, preprint #09208-86, M.S.R.I. Berkeley, Cal., July, 1986.

[20] A. Kasue, A Convergence Theorem for Riemannian Manifolds and Some Applications, to appear in Nagoya Math. J., Vol. 114, 1989. | MR | Zbl

[21] A. Kasue, Harmonic Functions with Growth Conditions on a Manifold of Asymptotically Nonnegative Curvature I, II, to appear.

[22] B. O'Neill, The Fundamental Equations for a Submersion (Mich. Math. J., Vol. 13, 1966, pp. 459-469). | MR | Zbl

[23] K. Shiohama, Busemann Functions and Total Curvature (Inventiones math., Vol. 53, 1979, pp. 281-297). | MR | Zbl

[24] K. Shiohama, Topology of a Complete Noncompact Manifold, Geometry of Geodesics and Related Topics, K. SHIOHAMA Ed., Advanced Studies in Pure Math., Vol. 3, 1984, pp. 423-450. | MR | Zbl

[25] V. A. Toponogov, Riemannian Spaces which Contain Straight Lines (Amer. Math. Soc. Transl. Ser., Vol. 37, 1964, pp. 287-290). | Zbl

[26] V. A. Toponogov, Riemannian Spaces Having their Curvature Bounded Below by a Positive Number (Amer. Math. Soc. Transl. Ser., Vol. 37, 1964, pp. 291-336). | Zbl

[27] H. Wu, An Elementary Method in the Study of Nonnegative Curvature (Acta Math., Vol. 142, 1979, pp. 57-78). | MR | Zbl

[28] H. Wu, Lectures at U. C. Berkeley, Spring, 1985.

Cité par Sources :