Semiconcave Functions in Alexandrov???s Geometry

The following is a compilation of some techniques in Alexandrov's geometry which are directly connected to convexity.

[1]  V. Sharafutdinov.  The Pogorelov-Klingenberg theorem for manifolds homeomorphic to Rn , 1977 .

[2]  V. Sharafutdinov.  The Pogorelov-Klingenberg theorem for manifolds that are homeomorphic to R , 1977 .

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

[4]  I. Nikolaev,et al.  Smoothness of the metric of spaces with bilaterally bounded curvature in the sense of A. D. Aleksandrov , 1983 .

[5]  Shortest lines on convex surfaces , 1984 .

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

[7]  Takao Yamaguchi.  Collapsing and pinching under a lower curvature bound , 1991 .

[8]  Almost nonpositively curved manifolds , 1991 .

[9]  K. Shiohama.  An Introduction to the geometry of Alexandrov spaces , 1993 .

[10]  Yu. G. Reshetnyak.  Two-Dimensional Manifolds of Bounded Curvature , 1993 .

[11]  P. Petersen,et al.  A radius sphere theorem , 1993 .

[12]  Splitting theorems for nonnegatively curved open manifolds with large ideal boundary , 1993 .

[13]  Y. Otsu,et al.  The Riemannian structure of Alexandrov spaces , 1994 .

[14]  P. Petersen,et al.  Spaces on and beyond the boundary of existence , 1995 .

[15]  C. Plaut.  Spaces of Wald-Berestovskii curvature bounded below , 1996 .

[16]  The asymptotic behavior of the set of rays , 1997 .

[17]  K. Grove,et al.  Metric constraints on exotic spheres via Alexandrov geometry. , 1997 .

[18]  G. Perelman.  Collapsing with No Proper Extremal Subsets , 1997 .

[19]  Y. Otsu.  Differential Geometric Aspects of Alexandrov Spaces , 1997 .

[20]  Arcwise Isometries,et al.  A Course in Metric Geometry , 2001 .

[21]  Restrictions on collapsing with a lower sectional curvature bound , 2001, math/0110087.

[22]  C. Plaut.  Metric Spaces of Curvature ⩾ k , 2001 .

[23]  Regularity of limits of noncollapsing sequences of manifolds , 2001, math/0109075.

[24]  R. Bishop,et al.  ℱK-convex functions on metric spaces , 2003 .

[25]  Polyhedral approximations of Riemannian manifolds , 2003 .

[26]  R. Bishop,et al.  Curvature bounds for warped products of metric spaces , 2004 .

[27]  Curves On Convex Surfaces , 2005 .

[28]  L. Ambrosio,et al.  Gradient Flows: In Metric Spaces and in the Space of Probability Measures , 2005 .

[29]  Alexander Lytchak,et al.  Open map theorem for metric spaces , 2006 .

[30]  A. Petrunin,et al.  An optimal lower curvature bound for convex hypersurfaces in Riemannian manifolds , 2013, 1303.5884.