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.

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

About the Author
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).


Book Information
ISBN 9781009288088
Author Pertti Mattila
Format Paperback
Page Count 182
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 280g
Dimensions(mm) 230mm * 153mm * 10mm