LIPSCHITZ-KILLING CURVATURES OF SELF-SIMILAR RANDOM FRACTALS

作者：Zaehle M^*

来源：Transactions of the American Mathematical Society, 2011, 363(5): 2663-2684.

DOI：10.1090/S0002-9947-2010-05198-0

• Self-similar random fractals
• curvatures
• Minkowski content
• branching random walks

For a large class of self-similar random sets F in R-d, geometric parameters C-k(F), k = 0, ... , d, are introduced. They arise as as. (average or essential) limits of the volume C-d(F(epsilon)), the surface area Cd-1 (F(epsilon)) and the integrals of general mean curvatures over the unit normal bundles C-k(F(epsilon)) of the parallel sets F(epsilon) of distance e rescaled by epsilon(D-k). as epsilon -> 0. Here D equals the as. Hausdorff dimension of F. The corresponding results for the expectations are also proved.

• 出版日期2011-5