Semiconcave functions in Alexandrov's geometry

Abstract

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

Minor updates in the old paper

References in corpus (3)

• An optimal lower curvature bound for convex hypersurfaces in Riemannian manifolds
• Polyhedral approximations of Riemannian manifolds
• Smoothing 3-dimensional polyhedral spaces

Cited by in corpus (35)

• A knot characterization and 1-connected nonnegatively curved 4-manifolds with circle symmetry
• Isometric actions on spheres with an orbifold quotient
• Metric-measure boundary and geodesic flow on Alexandrov spaces
• Structure of Submetries
• Fréchet Means for Distributions of Persistence diagrams
• Constancy of the dimension for RCD(K,N) spaces via regularity of Lagrangian flows
• Regular points of extremal subsets in Alexandrov spaces
• Curvature tensor of smoothable Alexandrov spaces
• Locally Lipschitz contractibility of Alexandrov spaces and its applications
• The coincidence of the homologies of integral currents and of integral singular chains, via cosheaves
• Alexandrov Spaces with Maximal Radius
• Application of good coverings to collapsing Alexandrov spaces
• The metric measure boundary of spaces with Ricci curvature bounded below
• Metric Geometry of Spaces of Persistence Diagrams
• Inradius collapsed manifolds
• Homotopy lifting property of an $e^{\epsilon }$-Lipschitz and co-Lipschitz map
• Self and partial gluing theorems for Alexandrov spaces with a lower curvature bound
• Convergence of Brownian motions on RCD(K,infty) spaces
• Quantitative stability of Gel'fand's inverse boundary problem
• Almost non-negatively curved 4-manifolds with torus symmetry
• Collapsing three-dimensional closed Alexandrov spaces with a lower curvature bound
• Noncritical maps on geodesically complete spaces with curvature bounded above
• Time-dependent gradient curves on CAT(0) spaces
• Improved regularity estimates for Lagrangian flows on $\text{RCD}(K,N)$ spaces
• Convergence of Brownian Motions on Metric Measure Spaces Under Riemannian Curvature-Dimension Conditions
• Good coverings of Alexandrov spaces
• Space-time convex functions and sectional curvature
• Extremal subsets in geodesically complete spaces with curvature bounded above
• The Injectivity Radius of Souls of Alexandrov Spaces
• Singularities of solutions of Hamilton-Jacobi equations
• Deformation of Hyperbolic Cone-Structures: Study of the non-Colapsing case
• Stability, Finiteness and Dimension Four
• Riemann curvature tensor on $\mathsf{RCD}$ spaces and possible applications
• Nonnegatively Curved Alexandrov Spaces with Souls of Codimension Two
• Delta-convex structure of the singular set of distance functions