Calculus of Variations and Geometric Measure Theory
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E. Durand-Cartagena - J. Tyson

Rectifiable curves in Sierpinski carpets

created by durandcar on 26 Mar 2010
modified on 23 Feb 2018


Published Paper

Inserted: 26 mar 2010
Last Updated: 23 feb 2018

Journal: Indiana Univ. Math. J.
Volume: 60
Pages: 285-310.
Year: 2011


We characterize the slopes of nontrivial line segments contained in self-similar Sierpinski carpets. The set of slopes is related to Farey sequences and the dynamics of punctured square toral billiards. Our results provide a first step towards a description of the rectifiable curves contained in such carpets.


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