Maximum density for the Sierpinski carpet

  • Authors:

  • Baoguo Jia

  • Affiliations:

  • School of Mathematics and Computational Science, Zhongshan University, Guangzhou, 510275, China

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2009

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Abstract

We prove that there exists a closed convex set obtaining the maximum density for the Sierpinski carpet S. That is, there exists a closed convex set V@?E"0, with |V|0, such that sup{@m(U)|U|^s:U@?E"0,is closed}=@m(V)|V|^s, where E"0 is defined in the introduction and @m denotes the unique self-similar probability measure on S. We give a reasonable description about the shape of V.