Accessible Requires Authentication Published by De Gruyter March 29, 2013

Fractal curvature measures of self-similar sets

Steffen Winter and Martina Zähle
From the journal

Abstract

Fractal Lipschitz-Killing curvature measures Ckf (F; ·), k = 0; ...; d, are determined for a large class of self-similar sets F in ℝd. They arise as weak limits of the appropriately rescaled classical Lipschitz-Killing curvature measures Ck(Fε; ·) from geometric measure theory of parallel sets Fε for small distances ε. Due to self-similarity the limit measures appear to be constant multiples of the normalized Hausdorff measures on F, and the constants agree with the corresponding total fractal curvatures Ckf (F) This provides information on the ’second order’ geometric fine structure of such fractals.


The first author was supported by grant DFG WE 1613/2-1 and the second author by grant DFG ZA 242/5-1.

Published Online: 2013-03-29
Published in Print: 2013-04

© 2013 by Walter de Gruyter GmbH & Co.