| Abstract: |
The recent construction by Lapidus and Pearse of the tubular zeta-function of a self-similar tiling as a certain
meromorphic function whose poles are the "complex dimensions" of the tiling and whose sum of residues
gives
the volume of its inner neighborhood, is an important breakthrough in the theory of fractals. As a first step beyond the
world of self-similar fractals, we define the tubular zeta-function of a self-affine tiling and apply it to a
higher-dimensional analogue of McMullen's generalized Sierpinski carpets. We use the fact that the volume of the
inner tube of a polytope is a piecewise polynomial function, which would be the inner counterpart of the well-known
classical Steiner formula for convex bodies.
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