Alexandrov geometry: foundations

by Stephanie Alexander, Vitali Kapovitch, and Anton Petrunin

The paper version is available at AMS; an older CC-BY version can be downloaded from arXiv. You can also download the source files and the latest version.

Table of contents:

Preliminaries
   1. Model plane
   2. Metric spaces
   3. Maps and functions
   4. Ultralimits
   5. Space of spaces
   6. The ghost of Euclid
   7. Dimension theory

Fundamentals
   8. Fundamentals of curvature bounded below
   9. Fundamentals of curvature bounded above
   10. Kirszbraun revisited
   11. Warped products
   12. Polyhedral spaces

Geodesics
   13. First order differentiation
   14. Dimension of CAT spaces
   15. Dimension of CBB spaces
   16. Gradient flow

Please email us comments/corrections/suggestions.

Misprints in the published version

• page 206, lines 9 and 11: in the displayed formulas (5) and (6) change the sign of the left-most term: \(\boldsymbol{d}_q\)... \(\to\) \(-\boldsymbol{d}_q\)...
• page 206, starting from lines \((-7)\), the calculations are incorrect; they are fixed in the updated version.