The magnitude of a metric space: from category theory to geometric measure theory

Chapters in this book

1. Frontmatter I
2. Contents V
3. New stability results for sequences of metric measure spaces with uniform Ricci bounds from below 1
4. Surface measures in infinite-dimensional spaces 52
5. An Overview of L¹ optimal transportation on metric measure spaces 98
6. On a conjecture of Cheeger 145
7. The magnitude of a metric space: from category theory to geometric measure theory 156
8. On the convexity of the entropy along entropic interpolations 194
9. Brief survey ∞-Poincaré inequality and existence ∞-harmonic functions 243
10. Metric measure limits of spheres and complex projective spaces 261
11. Scalar Curvature and Intrinsic Flat Convergence 288