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A compactification of a manifold with asymptotically nonnegative curvature

Atsushi Kasue

Annales scientifiques de l'École Normale Supérieure (1988)

  • Volume: 21, Issue: 4, page 593-622
  • ISSN: 0012-9593

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Kasue, Atsushi. "A compactification of a manifold with asymptotically nonnegative curvature." Annales scientifiques de l'École Normale Supérieure 21.4 (1988): 593-622. <http://eudml.org/doc/82238>.

@article{Kasue1988,
author = {Kasue, Atsushi},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {sectional curvature; asymptotically nonnegatively curved Riemannian manifold; Buseman function; exhaustion function},
language = {eng},
number = {4},
pages = {593-622},
publisher = {Elsevier},
title = {A compactification of a manifold with asymptotically nonnegative curvature},
url = {http://eudml.org/doc/82238},
volume = {21},
year = {1988},
}

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
PB - Elsevier
VL - 21
IS - 4
SP - 593
EP - 622
LA - eng
KW - sectional curvature; asymptotically nonnegatively curved Riemannian manifold; Buseman function; exhaustion function
UR - http://eudml.org/doc/82238
ER -

References

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  1. [1] U. ABRESCH, Lower Curvature Bounds, Toponogov's Theorem, and Bounded Topology (Ann. scient. Éc. Norm. Sup., Paris, Vol. 28, 1985, pp. 651-670). Zbl0595.53043MR87j:53058
  2. [2] M. T. ANDERSON, The Compactification of a Minimal Submanifold in Euclidean Space by the Gauss Map, preprint. 
  3. [3] W. BALLMANN, M. GROMOV and V. SCHROEDER, Manifolds of Nonpositive Curvature (Progress in Math., No. 61, Birkhöuser, Boston-Basel-Stuttgart, 1985). Zbl0591.53001MR87h:53050
  4. [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. Zbl0309.53035MR56 #16538
  5. [5] J. CHEEGER and D. GROMOLL, The Splitting Theorem for Manifolds of Nonnegative Ricci Curvature (J. Differential Geom., Vol. 6, 1971, pp. 119-128). Zbl0223.53033MR46 #2597
  6. [6] J. CHEEGER and D. GROMOLL, On the Structure of Complete Manifolds of Nonnegative Curvature (Ann. of Math., Vol. 96, 1974, pp. 413-443). Zbl0246.53049MR46 #8121
  7. [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). Zbl0484.53035MR83c:58083
  8. [8] H. DONNELY and P. LI, Heat Equation and Compactification of Complete Riemannian Manifolds (Duke Math. J., Vol. 51, 1984, pp. 667-673). Zbl0546.53029MR85h:58162
  9. [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). Zbl0598.53042MR87k:53090
  10. [10] R. E. GREENE and H. WU, C∞ Convex Functions and Manifolds of Positive Curvature (Acta Math., Vol. 137, 1976, pp. 209-245). Zbl0372.53019MR56 #16539
  11. [11] R. E. GREENE and H. WU, Function Theory on Manifolds which Possess a Pole (Lecture Notes in Math., No. 699, Springer-Verlag, 1979). Zbl0414.53043MR81a:53002
  12. [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). Zbl0415.31001MR80m:53055
  13. [13] R. E. GREENE and H. WU, Lipschitz Convergence of Riemannian Manifolds, (Pacific J. Math., Vol. 131, 1988, pp. 119-141). Zbl0646.53038MR89g:53063
  14. [14] M. GROMOV, Curvature, Diameter, and Betti Numbers (Comment. Math. Helv., Vol. 56, 1981, pp. 179-195). Zbl0467.53021MR82k:53062
  15. [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. Zbl0509.53034MR85e:53051
  16. [16] K. GROVE and K. SHIOHAMA, A Generalized Sphere Theorem (Ann. of Math., Vol. 106, 1977, pp. 201-211). Zbl0341.53029MR58 #18268
  17. [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). Zbl0518.53048MR85h:53031
  18. [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. Zbl0578.53029MR86j:53062
  19. [19] A. KASUE, On Manifolds of Asymptotically Nonnegative Curvature, preprint #09208-86, M.S.R.I. Berkeley, Cal., July, 1986. 
  20. [20] A. KASUE, A Convergence Theorem for Riemannian Manifolds and Some Applications, to appear in Nagoya Math. J., Vol. 114, 1989. Zbl0682.53042MR90g:53053
  21. [21] A. KASUE, Harmonic Functions with Growth Conditions on a Manifold of Asymptotically Nonnegative Curvature I, II, to appear. Zbl0745.31007
  22. [22] B. O'NEILL, The Fundamental Equations for a Submersion (Mich. Math. J., Vol. 13, 1966, pp. 459-469). Zbl0145.18602MR34 #751
  23. [23] K. SHIOHAMA, Busemann Functions and Total Curvature (Inventiones math., Vol. 53, 1979, pp. 281-297). Zbl0433.53050MR80m:53039
  24. [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. Zbl0551.53021MR85m:53043
  25. [25] V. A. TOPONOGOV, Riemannian Spaces which Contain Straight Lines (Amer. Math. Soc. Transl. Ser., Vol. 37, 1964, pp. 287-290). Zbl0138.42902
  26. [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). Zbl0136.42904
  27. [27] H. WU, An Elementary Method in the Study of Nonnegative Curvature (Acta Math., Vol. 142, 1979, pp. 57-78). Zbl0403.53022MR80c:53054
  28. [28] H. WU, Lectures at U. C. Berkeley, Spring, 1985. 

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