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

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

MathSciNet review:
0362137

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References | Similar Articles | Additional Information

**1.**J. Cheeger and D. Gromoll,*On the structure of complete manifolds of nonnegative curvature*, Ann. of Math. (2) 96 (1972), 413-443. MR 46 #8121. MR**309010****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 the plurisubharmonicity of geodesically convex functions*, Indiana Univ. Math. J. 22 (1973), 641-653. MR**422686****5.**R. E. Greene and H. Wu, "A theorem in complex geometric function theory," in*Value-distribution theory*. Part A, edited by R. O. Kujala and A. L. Vitter III, Dekker, New York, 1974, pp. 145-167. MR**352534****6.**R. E. Greene and H. Wu,*Integrals of subharmonic functions on manifolds of nonnegative curvature*, Invent. Math, (to appear). MR**382723****7.**D. Gromoll and W. Meyer,*On complete open manifolds of positive curvature*, Ann. of Math. (2) 90 (1969), 75-90. MR 40 #854. MR**247590****8.**W. A. Poor, Jr.,*Some results on nonnegatively curved manifolds*, Ph. D. Thesis, State University of New York at Stony Brook, 1973.**9.**R. Richberg,*Stetige streng pseudoconvexe functionen*, Math. Ann. 175 (1968), 257-286. MR**222334****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