Rectifiability

• Verfasst von: Mattila, Pertti [VerfasserIn]
• Titel: Rectifiability
• Titelzusatz: a survey
• Verf.angabe: Pertti Mattila (University of Helsinki)
• Verlagsort: Cambridge, United Kingdom ; New York, NY, USA ; Port Melbourne, Australia ; New Delhi, India
• Verlag: Cambridge University Press
• Jahr: 2023
• Umfang: 1 Online-Ressource (vii, 172 Seiten)
• Gesamttitel/Reihe: London Mathematical Society lecture note series ; 483
• Fussnoten: Title from publisher's bibliographic system (viewed on 10 Jan 2023)
• ISBN: 978-1-009-28805-7
• DOI: doi:10.1017/9781009288057
• Schlagwörter: (s)Rektifizierbare Menge / (s)Strom <Mathematik> / (s)Varifaltigkeit / (s)Heisenberg-Gruppe / (s)Singuläres Integral
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Mattila, Pertti, 1947 - : Rectifiability. - Cambridge, United Kingdom : Cambridge University Press, 2023. - vii, 172 Seiten
• K10plus-PPN: 183189923X
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

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.