Rectifiability: A Survey

ISBN-13: 9781009288088 / Angielski / Miękka / 2023 / 182 str.

Pertti (University of Helsinki) Mattila

Opis

A broad survey of the theory of rectifiability and its deep connections to numerous different areas of mathematics.

Spis treści

Introduction; 1. Preliminaries; 2. Rectifiable curves; 3. One-dimensional rectifiable sets; 4. Higher dimensional rectifiable sets; 5. Uniform rectifiability; 6. Rectifiability of measures; 7. Rectifiable sets in metric spaces; 8. Heisenberg and Carnot groups; 9. Bounded analytic functions and the Cauchy transform; 10. Singular integrals; 11. Harmonic measure and elliptic measures; 12. Sets of finite perimeter and functions of bounded variation; 13. Currents and varifolds; 14. Minimizers and quasiminimizers; 15. Rectifiability of singularities; 16. Miscellaneous topics related to rectifiability; References; Index.