engleski

Tube formulas for relative fractal drums in Euclidean spaces via Lapidus zeta functions

Relative fractal drums generalize the notion of fractal sets in Euclidean spaces of arbitrary dimension. We establish point wise and istributional fractal tube formulas for a large class of relative fractal drums. These fractal tube formulas are expressed as sums of residues of suitable meromorphic functions over the complex dimensions of the relative fractal drum under consideration (i.e., over the poles of its Lapidus zeta function which generalizes the well-known zeta function for fractal strings. These results generalize to higher dimensions the corresponding ones previously obtained for fractal strings by M. L. Lapidus and M. van Frankenhuijsen. We illustrate our results by several examples and apply them to obtain a new Minkowski measurability criterion.

fractal tube formula; Lapidus zeta function; Minkowski measurability

Poster je na konferenciji izložio Goran Radunović.