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A genealogy of noncompact manifolds of nonnegative curvature: history and logic. (English) Zbl 0884.53029
Grove, Karsten (ed.) et al., Comparison geometry. Cambridge: Cambridge University. Math. Sci. Res. Inst. Publ. 30, 99-134 (1997).
Summary: This article presents an approach to the theory of open manifolds of nonnegative sectional curvature via the calculus of nonsmooth functions. This analytical approach makes possible a very compact development of the by now classical theory. The article also gives a summary of the historical development of the subject of open manifolds of nonnegative sectional curvature and of related topics. Some very recent results are also discussed, including results of the author jointly with P. Petersen and S. H. Zhu on curvature decay [R. E. Greene, P. Petersen and S.-H. Zhu, Int. Math. Res. Not. 1994, 363-377 (1994; Zbl 0833.53037)].
For the entire collection see [Zbl 0871.00023].

MSC:
53C20 Global Riemannian geometry, including pinching
01A65 Development of contemporary mathematics
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