Convex functions on complete noncompact manifolds : differentiable structure
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 14 (1981) no. 4, pp. 357-367.
@article{ASENS_1981_4_14_4_357_0,
     author = {Greene, R. E. and Shiohama, K.},
     title = {Convex functions on complete noncompact manifolds : differentiable structure},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {357--367},
     publisher = {Elsevier},
     volume = {Ser. 4, 14},
     number = {4},
     year = {1981},
     doi = {10.24033/asens.1410},
     mrnumber = {83m:53057},
     zbl = {0488.57012},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/asens.1410/}
}
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Greene, R. E.; Shiohama, K. Convex functions on complete noncompact manifolds : differentiable structure. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 14 (1981) no. 4, pp. 357-367. doi : 10.24033/asens.1410. http://www.numdam.org/articles/10.24033/asens.1410/

[1] V. Bangert, Riemannische Mannigfaltigketten mit nicht-konstanter konvexer Funktioner (Archiv. der Math., Vol. 31, 1978, pp. 163-170). | MR | Zbl

[2] R. L. Bishop and B. O'Neill, Manifolds of Negative Curvature (Trans. Amer. Math. Soc., Vol. 145, 1969, pp. 1-49). | MR | Zbl

[3] S. S. Cairns, The Manifold Smoothing Problem (Bull. Amer. Math. Soc., Vol. 67, 1961, pp. 237-238). | MR | Zbl

[4] J. Cheeger and D. Gromoll, On the Structure of Complete Manifolds of Nonnegative Curvature (Ann. of Math., Vol. 96, 1972, pp. 413-443). | MR | Zbl

[5] R. E. Greene and K. Shiohama, Convex Functions on Complete Noncompact Riemannian Manifolds : Topological Structure (to appear Inventiones Math). | Zbl

[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). | MR | Zbl

[7] R. E. Greene and H. Wu, Integrals of Subharmonic Functions on manifolds of Nonnegative Culvature (Inventiiones Math., Vol. 27, 1974, pp. 265-298). | MR | Zbl

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

[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). | Numdam | MR | Zbl

[10] D. Gromoll and W. Meyer, On Complete Open Manifolds of Positive Curvature (Ann. of Math., Vol. 90, 1969, pp. 75-90). | MR | Zbl

[11] K. Grove and K. Shiohama, A Generalized Sphere Theorem (Ann. of Math., Vol. 106, 1975, pp. 201-211). | MR | Zbl

[12] M. Hirsch, On Combinatorial Submanifolds of Differentiable Manifolds (Comment. Math. Helv., Vol. 36, 1962, pp. 103-111). | EuDML | MR | Zbl

[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). | MR | Zbl

[14] J. Munkres, Elementary Differential Topology (Annals of Mathematics Studies, No. 54, Princeton University Press 1961, rev. ed. 1966). | MR | Zbl

[15] A. Phillips, Submersions of Open Manifolds Topology, Vol. 6, 1967, pp. 171-206. | MR | Zbl

[16] W. A. Poor, Some Results on Nonnegatively Curved Manifolds (J. Diff. Geometry, Vol. 9, 1974, pp. 583-600). | MR | Zbl

[17] K. Shiohama, Convex Sets and Convex Functions on Complete Manifolds (Proc. Intern. Cong. of Math., Helsinki, 1978). | MR | Zbl

[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). | MR | Zbl

[19] R. Walter, On the Metric Projection Onto Convex Sets in Riemannian Spaces (Archiv. Der. Math., Vol. 25, 1974, pp. 91-98). | MR | Zbl

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