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Cover: 9781009288088 | Rectifiability | Pertti Mattila | Taschenbuch | Englisch | 2023
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Rectifiability
Taschenbuch von Pertti Mattila
Sprache: Englisch

83,20 €

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Beschreibung
Rectifiable sets, measures, currents and varifolds are foundational concepts in geometric measure theory. The last four decades have seen the emergence of a wealth of connections between rectifiability and other areas of analysis and geometry, including deep links with the calculus of variations and complex and harmonic analysis. This short book provides an easily digestible overview of this wide and active field, including discussions of historical background, the basic theory in Euclidean and non-Euclidean settings, and the appearance of rectifiability in analysis and geometry. The author avoids complicated technical arguments and long proofs, instead giving the reader a flavour of each of the topics in turn while providing full references to the wider literature in an extensive bibliography. It is a perfect introduction to the area for researchers and graduate students, who will find much inspiration for their own research inside. This title is also available as open access on Cambridge Core.
Rectifiable sets, measures, currents and varifolds are foundational concepts in geometric measure theory. The last four decades have seen the emergence of a wealth of connections between rectifiability and other areas of analysis and geometry, including deep links with the calculus of variations and complex and harmonic analysis. This short book provides an easily digestible overview of this wide and active field, including discussions of historical background, the basic theory in Euclidean and non-Euclidean settings, and the appearance of rectifiability in analysis and geometry. The author avoids complicated technical arguments and long proofs, instead giving the reader a flavour of each of the topics in turn while providing full references to the wider literature in an extensive bibliography. It is a perfect introduction to the area for researchers and graduate students, who will find much inspiration for their own research inside. This title is also available as open access on Cambridge Core.
Über den Autor
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).
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2023
Fachbereich: Analysis
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Inhalt: Kartoniert / Broschiert
ISBN-13: 9781009288088
ISBN-10: 1009288083
Sprache: Englisch
Einband: Kartoniert / Broschiert
Autor: Mattila, Pertti
Hersteller: Cambridge University Press
Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße: 229 x 152 x 10 mm
Von/Mit: Pertti Mattila
Erscheinungsdatum: 12.01.2023
Gewicht: 0,273 kg
Artikel-ID: 122092343
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