Convex functions on complete noncompact manifolds : differentiable structure

R. E. Greene; K. Shiohama

Annales scientifiques de l'École Normale Supérieure (1981)

  • Volume: 14, Issue: 4, page 357-367
  • ISSN: 0012-9593

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Greene, R. E., and Shiohama, K.. "Convex functions on complete noncompact manifolds : differentiable structure." Annales scientifiques de l'École Normale Supérieure 14.4 (1981): 357-367. <http://eudml.org/doc/82079>.

@article{Greene1981,
author = {Greene, R. E., Shiohama, K.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {differentiable structure; Morse function; convex function on a complete C Riemannian manifold without minima; splitting Riemannian manifolds; diffeomorphic to a product of a manifold and the real line},
language = {eng},
number = {4},
pages = {357-367},
publisher = {Elsevier},
title = {Convex functions on complete noncompact manifolds : differentiable structure},
url = {http://eudml.org/doc/82079},
volume = {14},
year = {1981},
}

TY - JOUR
AU - Greene, R. E.
AU - Shiohama, K.
TI - Convex functions on complete noncompact manifolds : differentiable structure
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1981
PB - Elsevier
VL - 14
IS - 4
SP - 357
EP - 367
LA - eng
KW - differentiable structure; Morse function; convex function on a complete C Riemannian manifold without minima; splitting Riemannian manifolds; diffeomorphic to a product of a manifold and the real line
UR - http://eudml.org/doc/82079
ER -

References

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  1. [1] V. BANGERT, Riemannische Mannigfaltigketten mit nicht-konstanter konvexer Funktioner (Archiv. der Math., Vol. 31, 1978, pp. 163-170). Zbl0372.53021MR80e:53040
  2. [2] R. L. BISHOP and B. O'NEILL, Manifolds of Negative Curvature (Trans. Amer. Math. Soc., Vol. 145, 1969, pp. 1-49). Zbl0191.52002MR40 #4891
  3. [3] S. S. CAIRNS, The Manifold Smoothing Problem (Bull. Amer. Math. Soc., Vol. 67, 1961, pp. 237-238). Zbl0103.15801MR23 #A1383
  4. [4] J. CHEEGER and D. GROMOLL, On the Structure of Complete Manifolds of Nonnegative Curvature (Ann. of Math., Vol. 96, 1972, pp. 413-443). Zbl0246.53049MR46 #8121
  5. [5] R. E. GREENE and K. SHIOHAMA, Convex Functions on Complete Noncompact Riemannian Manifolds : Topological Structure (to appear Inventiones Math). Zbl0468.53033
  6. [6] R. E. GREENE and H. WU, On the Subharmonicity and Plurisubharmonicity of Geodesically Convex Functions (Indiana University Math. J., Vol. 22, 1973, pp. 641-653). Zbl0235.53039MR54 #10672
  7. [7] R. E. GREENE and H. WU, Integrals of Subharmonic Functions on manifolds of Nonnegative Culvature (Inventiiones Math., Vol. 27, 1974, pp. 265-298). Zbl0342.31003MR52 #3605
  8. [8] 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
  9. [9] R. E. GREENE and H. WU, C∞ Approximation of Convex, Subharmonic, and Plurisubharmonic Functions (Ann. scient. Ec. Norm. Sup., 4e Série, T. 12, 1979, pp. 47-84). Zbl0415.31001MR80m:53055
  10. [10] D. GROMOLL and W. MEYER, On Complete Open Manifolds of Positive Curvature (Ann. of Math., Vol. 90, 1969, pp. 75-90). Zbl0191.19904MR40 #854
  11. [11] K. GROVE and K. SHIOHAMA, A Generalized Sphere Theorem (Ann. of Math., Vol. 106, 1975, pp. 201-211). Zbl0341.53029MR58 #18268
  12. [12] M. HIRSCH, On Combinatorial Submanifolds of Differentiable Manifolds (Comment. Math. Helv., Vol. 36, 1962, pp. 103-111). Zbl0101.16101MR24 #A3658
  13. [13] R. C. KIRBY and L. C. SIEBENMANN, Foundational Essays on Topological Manifolds, Smoothings and Triangulations (Annals of Mathematics Studies, No. 88, Princeton University Press and University of Tokyo Press, 1977). Zbl0361.57004MR58 #31082
  14. [14] J. MUNKRES, Elementary Differential Topology (Annals of Mathematics Studies, No. 54, Princeton University Press 1961, rev. ed. 1966). Zbl0161.20201
  15. [15] A. PHILLIPS, Submersions of Open Manifolds Topology, Vol. 6, 1967, pp. 171-206. Zbl0204.23701MR34 #8420
  16. [16] W. A. POOR, Some Results on Nonnegatively Curved Manifolds (J. Diff. Geometry, Vol. 9, 1974, pp. 583-600). Zbl0292.53037MR51 #11351
  17. [17] K. SHIOHAMA, Convex Sets and Convex Functions on Complete Manifolds (Proc. Intern. Cong. of Math., Helsinki, 1978). Zbl0429.53029
  18. [18] R. WALTER, A Generalized Allendoerfer-Weil Formula and an Inequality of the Cohn-Vossen Type (J. Diff. Geometry, Vol. 10, 1975, pp. 167-180). Zbl0308.53042MR53 #9111
  19. [19] R. WALTER, On the Metric Projection Onto Convex Sets in Riemannian Spaces (Archiv. Der. Math., Vol. 25, 1974, pp. 91-98). Zbl0311.53054MR53 #1490

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