Tube Formulas for Self-Similar Fractals

  title={Tube Formulas for Self-Similar Fractals},
  author={Michel L. Lapidus and Erin P. J. Pearse},
Tube formulas (by which we mean an explicit formula for the volume of an ε-neighbourhood of a subset of a suitable metric space) have been used in many situations to study properties of the subset. For smooth submanifolds of Euclidean space, this includes Weyl’s celebrated results on spectral asymptotics, and the subsequent relation between curvature and spectrum. Additionally, a tube formula contains information about the dimension and measurability of rough sets. In convex geometry, the tube… CONTINUE READING