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.
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