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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  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
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  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
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