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Approximation theorems, $C^ \infty$ convex exhaustions and manifolds of positive curvature


Authors: R. E. Greene and H. Wu
Journal: Bull. Amer. Math. Soc. 81 (1975), 101-104
MSC (1970): Primary 53C20, 57D12; Secondary 53C55, 32F05, 31C05
MathSciNet review: 0362137
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References [Enhancements On Off] (What's this?)

  • 1. Jeff Cheeger and Detlef Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math. (2) 96 (1972), 413–443. MR 0309010
  • 2. R. E. Greene, Proper isometric imbeddings and Lipschitz continuous exhaustions (to appear).
  • 3. R. E. Greene and H. Wu, Curvature and complex analysis. I—III, Bull. Amer. Math. Soc. 77 (1971), 1045-1049; ibid. 78 (1972), 866-870; ibid. 79 (1973), 606-608. MR 44 #473; 45 #7657.
  • 4. R. E. Greene and H. Wu, On the subharmonicity and plurisubharmonicity of geodesically convex functions, Indiana Univ. Math. J. 22 (1972/73), 641–653. MR 0422686
  • 5. R. E. Greene and H. Wu, A theorem in complex geometric function theory, Value distribution theory (Proc. Tulane Univ. Program, Tulane Univ., New Orleans, La., 1972-1973) Dekker, New York, 1974, pp. 145–167. MR 0352534
  • 6. R. E. Greene and H. Wu, Integrals of subharmonic functions on manifolds of nonnegative curvature, Invent. Math. 27 (1974), 265–298. MR 0382723
  • 7. Detlef Gromoll and Wolfgang Meyer, On complete open manifolds of positive curvature, Ann. of Math. (2) 90 (1969), 75–90. MR 0247590
  • 8. W. A. Poor, Jr., Some results on nonnegatively curved manifolds, Ph. D. Thesis, State University of New York at Stony Brook, 1973.
  • 9. Rolf Richberg, Stetige streng pseudokonvexe Funktionen, Math. Ann. 175 (1968), 257–286 (German). MR 0222334
  • 10. R. Walter, Local and global properties of convex sets in Riemannian spaces, Proc. Sympos. Pure Math., vol. 27, Amer. Math. Soc. Providence, R. I. (to appear).

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DOI: https://doi.org/10.1090/S0002-9904-1975-13653-6