Tiling and spectral properties of near-cubic domains

Details Tiling and spectral properties of near-cubic domains Tiling and spectral properties of near-cubic domains

2001-06-02

arxiv.org/abs/math/0106012v2

Mathematics

Classical Analysis and ODEs

11 pages, 3 figures; added a counterexample in dimensions 3 and higher

Scientific paper

We prove that is a measurable domain tiles R or R^2 by translations, and if
it is "close enough" to a line segment or a square respectively, then it admits
a lattice tiling. We also prove a similar result for spectral sets in dimension
1, and give an example showing that there is no analogue of the tiling result
in dimensions 3 and higher.

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