Inextensible domains
Abstract
We develop a theory of planar, originsymmetric, 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 originsymmetric inextensible domains are exactly the originsymmetric 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 triangles, and show that it follows immediately from a result of Sas.
 Publication:

arXiv eprints
 Pub Date:
 January 2013
 DOI:
 10.48550/arXiv.1301.5880
 arXiv:
 arXiv:1301.5880
 Bibcode:
 2013arXiv1301.5880K
 Keywords:

 Mathematics  Metric Geometry;
 Mathematics  Differential Geometry;
 Mathematics  Functional Analysis;
 52C15 37J45
 EPrint:
 Final submitted manuscript. Geometriae Dedicata, 2013