Critical points of distance functions and applications to geometry

8. Introduction Critical points of distance functions Toponogov's theorem; first application:a Background on finiteness theorems Homotopy Finiteness Appendix. Some volume estimates Betti numbers and rank Appendix: The generalized Mayer-Vietoris estimate Rank, curvature and diameter Ricci curvature, volume and the Laplacian Appendix. The maximum principle Ricci curvature, diameter growth and finiteness of topological type. Appendix. Nonnegative Ricci curvature outside a compact set.

[1]  Peter Petersen,et al.  Bounding homotopy types by geometry , 1988 .

[2]  Michael T. Anderson,et al.  Complete Ricci-flat Kähler manifolds of infinite topological type , 1989 .

[3]  J. Cheeger,et al.  The splitting theorem for manifolds of nonnegative Ricci curvature , 1971 .

[4]  R. Greene,et al.  Lipschitz convergence of Riemannian manifolds. , 1988 .

[5]  Detlef Gromoll,et al.  On the Structure of Complete Manifolds of Nonnegative Curvature , 1972 .

[6]  Dagang Yang,et al.  Examples of manifolds of positive Ricci curvature , 1989 .

[7]  Loring W. Tu,et al.  Differential forms in algebraic topology , 1982, Graduate texts in mathematics.

[8]  A. Weinstein.  On the homotopy type of positively-pinched manifolds , 1967 .

[9]  J. Cheeger.  FINITENESS THEOREMS FOR RIEMANNIAN MANIFOLDS. , 1970 .

[10]  T. Sakai.  Comparison and Finiteness Theorems in Riemannian Geometry , 1984 .

[11]  U. Abresch,et al.  On complete manifolds with nonnegative Ricci curvature , 1990 .

[12]  Stanley Peters.  Convergence of riemannian manifolds , 1987 .

[13]  M. Berger.  Les variétés riemanniennes (1/4)-pincées , 1960 .

[14]  E. Calabi.  An extension of E. Hopf’s maximum principle with an application to Riemannian geometry , 1958 .

[15]  U. Abresch,et al.  Lower curvature bounds, Toponogov's theorem, and bounded topology. II , 1985 .

[16]  J. Eschenburg,et al.  An elementary proof of the Cheeger-Gromoll splitting theorem , 1984 .

[17]  Detlef Gromoll,et al.  The structure of complete manifolds of nonnegative curvature , 1968 .

[18]  Zhong-dong Liu.  Ball covering on manifolds with nonnegative Ricci curvature near infinity , 1992 .

[19]  Michael T. Anderson.  Short geodesics and gravitational instantons , 1990 .

[20]  Controlled topology in geometry , 1989 .

[21]  The relation between the laplacian and the diameter for manifolds of non-negative curvature , 1968 .

[22]  Michael Gromov,et al.  Curvature, diameter and betti numbers , 1981 .

[23]  Stefan Peters,et al.  Cheeger's finiteness theorem for diffeomorphism classes of Riemannian manifolds. , 1984 .

[24]  Karsten Grove,et al.  A generalized sphere theorem , 1977 .