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  3. Rectifiability
  • Cited by 6
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    • Publisher:
      Cambridge University Press
      Publication date:
      December 2022
      January 2023
      ISBN:
      9781009288057
      9781009288088
      DOI:
      https://doi.org/10.1017/9781009288057
      Creative Commons:
      Creative Common License - CC Creative Common License - BY Creative Common License - NC
      This content is Open Access and distributed under the terms of the Creative Commons Attribution licence CC-BY-NC 4.0.
      https://creativecommons.org/creativelicenses
      Dimensions:
      Weight & Pages:
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.28kg, 182 Pages
      • Subjects:
      Mathematics (general), Mathematics, Real and Complex Analysis, Geometry and Topology
      Series:
      London Mathematical Society Lecture Note Series (483)
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    Subjects:
    Mathematics (general), Mathematics, Real and Complex Analysis, Geometry and Topology
    Series:
    London Mathematical Society Lecture Note Series (483)
    Information

    Book description

    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.

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    Contents

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    Contents
    • Frontmatter
      pp i-iv
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    • Contents
      pp v-viii
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    • Introduction
      pp 1-2
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    • 1 - Preliminaries
      pp 3-5
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    • 2 - Rectifiable Curves
      pp 6-8
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    • 3 - One-Dimensional Rectifiable Sets
      pp 9-17
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    • 4 - Higher-Dimensional Rectifiable Sets
      pp 18-36
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    • 5 - Uniform Rectifiability
      pp 37-46
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    • 6 - Rectifiability of Measures
      pp 47-51
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    • 7 - Rectifiable Sets in Metric Spaces
      pp 52-62
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    • 8 - Heisenberg and Carnot Groups
      pp 63-77
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    • 9 - Bounded Analytic Functions and the Cauchy Transform
      pp 78-88
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    • 10 - Singular Integrals
      pp 89-98
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    • 11 - Harmonic Measure and Elliptic Measures
      pp 99-106
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    • 12 - Sets of Finite Perimeter and Functions of Bounded Variation
      pp 107-114
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    • 13 - Currents and Varifolds
      pp 115-124
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    • 14 - Minimizers and Quasiminimizers
      pp 125-128
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    • 15 - Rectifiability of Singularities
      pp 129-142
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    • 16 - Miscellaneous Topics Related to Rectifiability
      pp 143-148
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    • References
      pp 149-170
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    • Index
      pp 171-172
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