Tube formulas for self-similar fractals

zbMath1157.28001arXiv0711.0173MaRDI QIDQ3545431

Michel L. Lapidus, Erin P. J. Pearse

Publication date: 10 December 2008

Full work available at URL: https://arxiv.org/abs/0711.0173

Mathematics Subject Classification ID

Polyhedra and polytopes; regular figures, division of spaces (51M20) Metric geometry (51F99) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Length, area, volume, other geometric measure theory (28A75) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Integral geometry (53C65) Fractals (28A80) Mixed volumes and related topics in convex geometry (52A39) Dimension theory in general topology (54F45) Polytopes and polyhedra (52B99) Length, area and volume in real or complex geometry (51M25) Convexity of real functions of several variables, generalizations (26B25) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Tilings in (2) dimensions (aspects of discrete geometry) (52C20) Tilings in (n) dimensions (aspects of discrete geometry) (52C22) Random convex sets and integral geometry (aspects of convex geometry) (52A22) Convex sets without dimension restrictions (aspects of convex geometry) (52A05) Combinatorial complexity of geometric structures (52C45)

Related Items (9)

Inner tube formulas for polytopes ⋮ Fractal strings and multifractal zeta functions ⋮ Lattice-type self-similar sets with pluriphase generators fail to be Minkowski measurable ⋮ Towards quantized number theory: spectral operators and an asymmetric criterion for the Riemann hypothesis ⋮ Geometry of canonical self-similar tilings ⋮ Fractal zeta functions and complex dimensions of relative fractal drums ⋮ Self-similar \(p\)-adic fractal strings and their complex dimensions ⋮ Pointwise tube formulas for fractal sprays and self-similar tilings with arbitrary generators ⋮ An overview of complex fractal dimensions: from fractal strings to fractal drums, and back

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