Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators

DOI10.1016/j.aim.2011.03.004zbMath1274.28016arXiv1006.3807OpenAlexW2964013224MaRDI QIDQ555589

Erin P. J. Pearse, Steffen Winter, Michel L. Lapidus

Publication date: 25 July 2011

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.3807

zbMATH Keywords

generating functionzeta functionsinradiuscurvaturesSteiner formulacomplex dimensionsfractal stringself-similar tilingfractal curvaturesfractal sprayfractal tube formulalattice and nonlatticeMinkowski measurability and contentscaling and integer dimensionsscaling and tubular zeta functionstube formula

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Fractals (28A80) Length, area and volume in real or complex geometry (51M25) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Tilings in (n) dimensions (aspects of discrete geometry) (52C22)

Related Items (26)

Inner tube formulas for polytopes ⋮ Minkowski content and fractal curvatures of self-similar tilings and generator formulas for self-similar sets ⋮ Lattice-type self-similar sets with pluriphase generators fail to be Minkowski measurable ⋮ Complex dimensions of fractals and meromorphic extensions of fractal zeta functions ⋮ Tube formulas for self-similar and graph-directed fractals ⋮ \(h\)-Laplacians on singular sets ⋮ Scaling exponents of curvature measures ⋮ Towards quantized number theory: spectral operators and an asymmetric criterion for the Riemann hypothesis ⋮ Minkowski content and local Minkowski content for a class of self-conformal sets ⋮ Truncated infinitesimal shifts, spectral operators and quantized universality of the Riemann zeta function ⋮ Fractal tube formulas and a Minkowski measurability criterion for compact subsets of Euclidean spaces ⋮ Book review of: M. Lapidus et al., Fractal zeta functions and fractal drums. Higher-dimensional theory of complex dimensions ⋮ Distance and tube zeta functions of fractals and arbitrary compact sets ⋮ A survey of complex dimensions, measurability, and the lattice/nonlattice dichotomy ⋮ Multifractal spectra and multifractal zeta-functions ⋮ Geometry of canonical self-similar tilings ⋮ Fractal zeta functions and complex dimensions of relative fractal drums ⋮ Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators ⋮ Tube formulas and complex dimensions of self-similar tilings ⋮ The Shape of Anisotropic Fractals: Scaling of Minkowski Functionals ⋮ Fractal Zeta Functions and Complex Dimensions: A General Higher-Dimensional Theory ⋮ Besov class via heat semigroup on Dirichlet spaces. III: BV functions and sub-Gaussian heat kernel estimates ⋮ \(p\)-adic fractal strings of arbitrary rational dimensions and Cantor strings ⋮ An overview of complex fractal dimensions: from fractal strings to fractal drums, and back ⋮ Stability Properties of Fractal Curvatures ⋮ Tube volumes via functional equations

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