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Greene, R. E.; Shiohama, K.

Convex functions on complete noncompact manifolds: Topological structure. (English) Zbl 0468.53033

Invent. Math. 63, 129-157 (1981).
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scan of Zbl 0468.53033

Cited in 5 Reviews
Cited in 29 Documents

MSC:

53C20 Global Riemannian geometry, including pinching

Keywords:

convex functions; complete noncompact manifolds

Citations:

Zbl 0372.53021; Zbl 0191.520
Cite Review PDF
Full Text: DOI EuDML

References:

[1] Bangert, V.: Riemannsche Mannigfaltigkeiten mit nicht-konstanter konvexer Funktionen. Archiv der Math.31, 163-170 (1978) · Zbl 0372.53021 · doi:10.1007/BF01226433
[2] Bangert, V.: Totally convex sets in complete Riemannian manifolds, Preprint · Zbl 0479.53032
[3] Bishop, R., O’Neill, B.: Manifolds of negative curvature. Trans. Amer. Math. Soc.145, 1-49 (1969) · Zbl 0191.52002 · doi:10.1090/S0002-9947-1969-0251664-4
[4] Busemann, H.: The geometry of geodesics. New York: Academic Press, 1955 · Zbl 0112.37002
[5] Cheeger, J., Gromoll, D.: On the structure of complete manifods on nonnegative curvature. Ann. of Math.96, 413-443 (1972) · Zbl 0246.53049 · doi:10.2307/1970819
[6] Cheeger, J., Gromoll, D.: The splitting theorem for manifolds of nonnegative Ricci curvature. J. Diff. Geometry6, 119-128 (1971) · Zbl 0223.53033
[7] Greene, R.E., Shiohama, K.: Riemannian manifolds having a nowhere constant convex function. Notices Amer. Math. Soc. Vol.26, No. 2 a-223 (1979)
[8] Greene, R.E., Shiohama, K.: Convex functions on complete noncompact manifolds: Differentiable structure, to appear · Zbl 0488.57012
[9] Greene, R.E., Wu, H.: On the subharmonicity and plurisubharmonicity of geodesically convex functions. Indiana Univ. Math. J.22, 641-653 (1973) · Zbl 0235.53039 · doi:10.1512/iumj.1973.22.22052
[10] Greene, R.E., Wu, H.: Integrals of subharmonic functions on manifolds of nonnegative curvature. Inventiones math27, 265-298 (1974) · Zbl 0342.31003 · doi:10.1007/BF01425500
[11] Greene, R.E., Wu, H.:C ? convex functions and manifolds of positive curvature. Acta Math.137, 209-245 (1976) · Zbl 0372.53019 · doi:10.1007/BF02392418
[12] Greene, R.E., Wu, H.:C ? approximation of convex, subharmonic, and plurisubharmonic functions. Ann. scient. Ec. Norm. Sup. 4e serie t.12, 47-84 (1979)
[13] Gromoll, D., Meyer, W.: On complete open manifolds of positive curvature. Ann. of Math.90, 75-90 (1969) · Zbl 0191.19904 · doi:10.2307/1970682
[14] Kobayashi, S., Nomizu, K.: Foundations of differential geometry, II. New York: Wiley-Interscience, 1969 · Zbl 0175.48504
[15] Narasimhan, R.: Analysis on real and complex manifolds. Amsterdam: North-Holland, 1968 · Zbl 0188.25803
[16] Poor, W.A.: Some results on nonegatively curved manifolds. J. Diff. Geometry9, 583-600 (1974) · Zbl 0292.53037
[17] Walter, R.: A generalized Allendoerfer-Weil formula and an inequality of the Cohn-Vossen type. J. Diff. Geometry10, 167-180 (1975) · Zbl 0308.53042
[18] Walter, R.: On the metric projection onto convex sets in Riemannian spaces. Archiv d. Math.25, 91-98 (1974) · Zbl 0311.53054 · doi:10.1007/BF01238646
[19] Whitehead, J.H.C.: Convex regions in the geometry of paths. Quartery J. Math.2(3), 33-42 · Zbl 0004.13102
[20] Yau, S.T.: Nonexistence of continuous convex functions on certain Riemannian manifolds. Math. Ann.207, 269-270 (1974) · doi:10.1007/BF01351342
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