References
Bangert, V.: Über die Approximation von lokal konvexen Mengen. Manuscr. Math.25, 397–420 (1978)
Berger, M.: Les variétés riemannienes (1/4)-pincées. Ann. Sc. Norm. Super. Pisa, III.14, 161–170 (1960)
Cheeger, J., Ebin, D.G.: Comparison theorems in Riemannian geometry. Amsterdam: North Holland 1975
Cheeger, J., Gromoll, D.: On the structure of complete manifolds of nonnegative curvature. Ann. Math.96, 413–443 (1972)
Eschenburg, J.H., O'Sullivan, J.J.: Jacobi tensors and Ricci curvature. Math. Ann.252, 1–26 (1980)
Eschenburg, J.H., Heintze, E.: An elementary proof of the Cheeger-Gromoll Splitting Theorem. Ann. Glob. Analysis and Geometry2, 141–151 (1984)
Green, L.W.: A theorem of E. Hopf. Mich. Math. J.5, 31–34 (1958)
Greene, R.E., Wu, H.: On the subharmonicity and plurisubharmonicity of geodesically convex functions. Indiana Univ. Math. J.22, 641–653 (1973)
Greene, R.E., Wu, H.:C ∞ convex functions and manifolds of positive curvature. Acta Math.137, 209–245 (1976)
Gromoll, D., Klingenberg, W., Meyer, W.: Riemannsche Geometrie im Gro\en. Lect. Notes Math.55 (1968)
Gromoll, D., Meyer, W.: On complete open manifolds of positive curvature. Ann. Math.90, 75–90 (1969)
Grove, K., Shiohama, K.: A generalized sphere theorem. Ann. Math.106, 201–211 (1977)
Guilleman, V., Pollack, A.: Differential Topology. Englewood Cliffs: Prentice Hall 1974
Hadamard, J.: Sur certaines propriétés des trajectories en dynamique. J. Math. Pures Appl. (5)3, 331–387 (1897)
Hopf, H.: Differential Geometry in the Large, Ch. IV: Hadamard's characterization of the ovaloids. Stanford Lectures 1956. Lect. Notes Math.1000, 1983
Jost, J., Karcher, H.: Geometrische Methoden zur Gewinnung von a-priori-Schranken für harmonische Abbildungen. Manuscr. Math.40, 27–77 (1982)
Klingenberg, W.: Über Riemannsche Mannigfaltigkeiten mit positiver Krümmung. Commun. Math. Helv.35, 47–54 (1961)
Kobayashi, S., Wu, H.: Complex differential geometry. DMV-Seminar Bd. 3. Basel: Birkhäuser 1983
Milnor, J.: Morse theory. Ann. Math. Stud.51, Princeton, N.J. 1963
Wu, H.: An elementary method in the study of nonnegative curvature. Acta Math.142, 57–78 (1979)
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Dedicated to Wilhelm Klingenberg
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Eschenburg, J.H. Local convexity and nonnegative curvature —Gromov's proof of the sphere theorem. Invent Math 84, 507–522 (1986). https://doi.org/10.1007/BF01388744
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DOI: https://doi.org/10.1007/BF01388744