Alexandrov geometry: foundations

by Stephanie Alexander, Vitali Kapovitch, and Anton Petrunin

Links: paper version at AMS - Erratum - CC-BY version at arXiv - the latest version - the source files at GitHub.

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.

Structure and tools
13. First order differentiation.    14. Dimension of CAT spaces.    15. Dimension of CBB spaces.    16. Gradient flow.

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