Lomonosov Moscow State University
This four-lecture series develops the basic language of Gromov–Hausdorff geometry, from definitions and compactness questions to structural properties of the ambient space of compact metric spaces.
Course Program
Alexander O. Ivanov
Introduction and basic properties of Gromov–Hausdorff distance
Lecture 1
Hausdorff and Gromov–Hausdorff distances
Lecture 2
Properties of the Gromov–Hausdorff distance
Lecture 3
Compact metric spaces in GH-topology
Lecture 4
Local and global isometries of space ℳ
Detailed contents
Lecture outlines
Lecture 1
Hausdorff and Gromov–Hausdorff distances
- Definition and basic properties of the Hausdorff distance
- The Hausdorff distance is a generalized metric on closed subsets
- Gromov–Hausdorff distance between metric spaces
- GH-distance in terms of embeddings
- GH-distance in terms of correspondences
- Elementary properties of the GH-distance
Lecture 2
Properties of the Gromov–Hausdorff distance
- GH-distance is a generalized pseudometric
- Completeness and intrinsicness of the GH-distance
- Technique of irreducible correspondences
- Examples
- 3-point spaces
- Spaces with one non-zero distance (simplexes)
- Continuity of metric characteristics and closeness of subclasses
- Diameter, density, covering numbers
- Separable spaces, totally bounded spaces, compact spaces
- Uniform convergence of metrics