Inextensible domains

@article{Kallus2013InextensibleD,
  title={Inextensible domains},
  author={Yoav Kallus},
  journal={Geometriae Dedicata},
  year={2013},
  volume={173},
  pages={177-184}
}
  • Yoav Kallus
  • Published 24 January 2013
  • Mathematics
  • Geometriae Dedicata
We develop a theory of planar, origin-symmetric, convex domains that are inextensible with respect to lattice covering, that is, domains such that augmenting them in any way allows fewer domains to cover the same area. We show that origin-symmetric inextensible domains are exactly the origin-symmetric convex domains with a circle of outer billiard triangles. We address a conjecture by Genin and Tabachnikov about convex domains, not necessarily symmetric, with a circle of outer billiard… 

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We consider the problem of identifying the worst point-symmetric shape for covering n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}

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