Characterization of Minkowski measurability in terms of surface area

@article{Rataj2013CharacterizationOM,
  title={Characterization of Minkowski measurability in terms of surface area},
  author={J. Rataj and S. Winter},
  journal={Journal of Mathematical Analysis and Applications},
  year={2013},
  volume={400},
  pages={120-132}
}
  • J. Rataj, S. Winter
  • Published 2013
  • Mathematics
  • Journal of Mathematical Analysis and Applications
  • Abstract The r -parallel set to a set A in Euclidean space consists of all points with distance at most r from A . Recently, the asymptotic behaviour of volume and surface area of the parallel sets as r tends to 0 has been studied and some general results regarding their relations have been established. Here we complete the picture regarding the resulting notions of Minkowski content and S -content. In particular, we show that a set is Minkowski measurable if and only if it is S -measurable, i… CONTINUE READING
    Localization results for Minkowski contents
    2

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 18 REFERENCES
    Lower S-dimension of fractal sets
    4
    Generalized Minkowski Content and the Vibrations of Fractal Drums and Strings
    7
    Curvature measures and fractals
    48
    Analysis of Minkowski contents of fractal sets and applications.
    45
    A local Steiner–type formula for general closed sets and applications
    108
    The Riemann Zeta-Function and the One-Dimensional Weyl-Berry Conjecture for Fractal Drums
    172
    Curves and Fractal Dimension
    401
    Complex Dimensions and Zeta Functions: Geometry and spectra of fractal strings
    144
    Fluctuation Results for the Wiener Sausage
    56