Functions of substitution tilings as a Jacobian
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- by Yaar Solomon PDF
- Proc. Amer. Math. Soc. 141 (2013), 3853-3863 Request permission
Abstract:
A tiling $\tau$ of the Euclidean space gives rise to a function $f_\tau$, which is constant $1/\left |{T}\right |$ on the interior of every tile $T$. In this paper we give a local condition to know when $f_\tau$, which is defined by a primitive substitution tiling of the Euclidean space, can be realized as a Jacobian of a biLipschitz homeomorphism of $\mathbb {R}^d$. As an example we show that this condition holds for any star-shaped substitution tiling of $\mathbb {R}^2$. In particular, the result holds for any Penrose tiling.References
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Additional Information
- Yaar Solomon
- Affiliation: Department of Mathematics, Ben-Gurion University of The Negev, Beer-Sheva, Israel
- Email: yaars@bgu.ac.il
- Received by editor(s): August 17, 2010
- Received by editor(s) in revised form: January 12, 2012
- Published electronically: July 16, 2013
- Additional Notes: This research was supported by the Israel Science Foundation, grant No. 190/08
- Communicated by: Michael Wolf
- © Copyright 2013 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 141 (2013), 3853-3863
- MSC (2010): Primary 46-XX, 51-XX
- DOI: https://doi.org/10.1090/S0002-9939-2013-11663-1
- MathSciNet review: 3091774