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 | Similar Articles | Additional Information

**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