This short book gives an overview of rectifiability and its deep connections with surprisingly large parts of mathematics. It avoids long technical arguments in favour of the big picture, with full references given via an extensive bibliography, giving readers an easily digestible presentation of this wide and active field.
This short book gives an overview of rectifiability and its deep connections with surprisingly large parts of mathematics. It avoids long technical arguments in favour of the big picture, with full references given via an extensive bibliography, giving readers an easily digestible presentation of this wide and active field.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Pertti Mattila is Professor Emeritus in the Department of Mathematics at the University of Helsinki. He has worked in geometric measure theory and related fields for nearly fifty years. He is the author of 'Geometry of Sets and Measures in Euclidean Spaces' (1999) and 'Fourier Analysis and Hausdorff Dimension' (2015).
Inhaltsangabe
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.