Download Comparison geometry by Karsten Grove, Peter Petersen PDF

By Karsten Grove, Peter Petersen

This booklet files the hot specialise in a department of Riemannian geometry known as comparability Geometry. the straightforward suggestion of evaluating the geometry of an arbitrary Riemannian manifold with the geometries of continuous curvature areas has noticeable a major evolution lately. This quantity is an up to date mirrored image of the hot improvement concerning areas with reduce (or two-sided) curvature bounds. The content material displays probably the most fascinating actions compared geometry in the course of the yr and particularly of the Mathematical Sciences examine Institute's workshop dedicated to the topic. This quantity beneficial properties either survey and study articles. It additionally presents whole proofs: in a single case, a brand new, unified method is gifted and new proofs are provided. This quantity should be a important resource for complex researchers and people who desire to know about and give a contribution to this pretty topic.

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20 (1987), 227–239. [Gromoll and Grove 1988] D. Gromoll and K. Grove, “The low-dimensional metric foliations of Euclidean spheres”, J. Diff. Geom. 28 (1988), 143–156. [Gromoll and Meyer 1969] D. Gromoll and W. Meyer, “On differentiable functions with isolated critical points”, Topology 8 (1969), 361–369. [Gromoll and Meyer 1974] D. Gromoll and W. Meyer, “An exotic sphere with nonnegative sectional curvature”, Ann. of Math. 100 (1974), 401–408. INJECTIVITY RADIUS ESTIMATES AND SPHERE THEOREMS 45 [Gromov 1981a] M.

Berger 1960a] M. Berger, “Sur quelques vari´et´es Riemanniennes suffisamment pinc´ees”, Bull. Soc. math. France 88 (1960), 57–71. [Berger 1960b] M. Berger, “Les vari´et´es riemanniennes 14 -pinc´ees”, Ann. Scuola Norm. Sup. Pisa 14 (1960), 161–170. [Berger 1961] M. Berger, “Les vari´et´es riemanniennes homog`enes normales simplement connexes ` a courbure strictement positive”, Ann. Scuola Norm. Sup. Pisa 15 (1961), 179–246. [Berger 1962a] M. Berger, “On the diameter of some Riemannian manifolds”, Technical report, Univ.

164 (1966), 317–327. -H. Eschenburg, “New examples of manifolds with strictly positive curvature”, Invent. Math. 66 (1982), 469–480. -H. Eschenburg, “Freie isometrische Aktionen auf kompakten Liegruppen mit positiv gekr¨ ummten Orbitr¨ aumen”, Schriftenreihe Math. Inst. Univ. M¨ unster 32 (1984). -H. Eschenburg, “Inhomogeneous spaces of positive curvature”, Diff. Geom. Appl. 2 (1992), 123–132. [Freedman 1982] M. H. Freedman, “The topology of four-dimensional manifolds”, J. Diff. Geom. 17 (1982), 357–453.

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