Advanced Studies in Pure Mathematics

Remarks on non-diagonality conditions for Sierpinski carpets

Naotaka Kajino

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Abstract

We prove the equivalence of three different formulations of non-diagonality for Sierpinski carpets given by Barlow, Bass, Kumagai and Teplyaev [5], by Hino [10] and by Kigami [12]. We also derive some geometric property of Sierpinski carpets from the non-diagonality. As an application, we give a simpler treatment of a criterion stated in Kigami [12, Section 3.4] for the volume doubling property of self-similar measures on Sierpinski carpets.

Article information

Source
Probabilistic Approach to Geometry, M. Kotani, M. Hino and T. Kumagai, eds. (Tokyo: Mathematical Society of Japan, 2010), 231-241

Dates
Received: 15 January 2009
Revised: 11 June 2009
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543086321

Digital Object Identifier
doi:10.2969/aspm/05710231

Mathematical Reviews number (MathSciNet)
MR2648262

Zentralblatt MATH identifier
1202.28010

Subjects
Primary: 28A80: Fractals [See also 37Fxx] 31C25: Dirichlet spaces 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]

Keywords
Generalized Sierpinski carpet non-diagonality volume doubling property self-similar measure

Citation

Kajino, Naotaka. Remarks on non-diagonality conditions for Sierpinski carpets. Probabilistic Approach to Geometry, 231--241, Mathematical Society of Japan, Tokyo, Japan, 2010. doi:10.2969/aspm/05710231. https://projecteuclid.org/euclid.aspm/1543086321


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