Fractal curvature measures of self-similar sets

Autor:	Winter, Steffen, Zähle, Martina
Rok vydání:	2010
Předmět:	Mathematics - Metric Geometry Mathematics - Differential Geometry Primary 28A75 28A80 Secondary 28A78 53C65
Druh dokumentu:	Working Paper
Popis:	Fractal Lipschitz-Killing curvature measures C^f_k(F,.), k = 0, ..., d, are determined for a large class of self-similar sets F in R^d. They arise as weak limits of the appropriately rescaled classical Lipschitz-Killing curvature measures C_k(F_r,.) from geometric measure theory of parallel sets F_r for small distances r>0. 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 C^f_k(F). This provides information on the 'second order' geometric fine structure of such fractals. Comment: 13 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1007.0696 Zobrazit plný text záznamu View this record from Arxiv