Pertti Mattila

Rectifiability (eBook, PDF)

A Survey

• Format: PDF

Produktbeschreibung

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

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 12. Januar 2023
• Englisch
• ISBN-13: 9781009288095
• Artikelnr.: 70914596

Autorenporträt

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.