Fractal Tube Formulas

  • Michel L. Lapidus
  • Machiel van Frankenhuijsen
Part of the Springer Monographs in Mathematics book series (SMM)


In this chapter, we obtain (in Section 8.1) a distributional formula for the volume of the tubular neighborhoods of the boundary of a fractal string, called a tube formula. In Section 8.1.1, under more restrictive assumptions, we also derive a tube formula that holds pointwise. In Section 8.3, we then deduce from these formulas a new criterion for the Minkowski measurability of a fractal string, in terms of its complex dimensions.


Explicit Formula Complex Dimension Tubular Neighborhood Complex Dimen Minkowski Dimension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Michel L. Lapidus
    • 1
  • Machiel van Frankenhuijsen
    • 2
  1. 1.Department of MathematicsUniversity of California, RiversideRiversideUSA
  2. 2.Department of MathematicsUtah Valley UniversityOremUSA

Personalised recommendations