Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media New York
About this chapter
Cite this chapter
Lapidus, M.L., van Frankenhuijsen, M. (2013). Fractal Tube Formulas. In: Fractal Geometry, Complex Dimensions and Zeta Functions. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-2176-4_8
Download citation
DOI: https://doi.org/10.1007/978-1-4614-2176-4_8
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-2175-7
Online ISBN: 978-1-4614-2176-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)