Tubular Neighborhoods and Minkowski Measurability

Michel L. Lapidus () and Machiel van Frankenhuysen ()
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Michel L. Lapidus: University of California, Department of Mathematics
Machiel van Frankenhuysen: University of California, Department of Mathematics

Chapter 6 in Fractal Geometry and Number Theory, 2000, pp 143-161 from Springer

Abstract: Abstract In this chapter, we apply our extended distributional explicit formula (Theorem 4.20, derived in Section 4.4.2) to obtain a formula for the volume of the tubular neighborhoods of the boundary of a fractal string. (See Section 6.1.) In Section 6.2, we then deduce from this formula a new criterion for the Minkowski measurability of a fractal string, in terms of its complex dimensions. This completes and extends the earlier criterion obtained in [LapPol-2].

Keywords: Complex Dimension; Tubular Neighborhood; Gauge Function; Sierpinski Gasket; Weyl Curvature (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1007/978-1-4612-5314-3_7

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