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Tube formulas for selfsimilar fractal  Michel L. Lapidus
; Erin P. J. Pearse
;  Date: 
1 Nov 2007  Abstract:  Tube formulas (by which we mean an explicit formula for the volume of an
$epsilon$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 formula of a convex
subset of Euclidean space allows for the definition of certain curvature
measures. These measures describe the curvature of sets which are not too
irregular to support derivatives. In this survey paper, we describe some recent
advances in the development of tube formulas for selfsimilar fractals, and
their applications and connections to the other topics mentioned here.  Source:  arXiv, 0711.0173  Services:  Forum  Review  PDF  Favorites 


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