Monohedral Tilings of a Convex Disc with a Smooth Boundary

Abstract

In this paper we give a complete description about normal monohedral tilings of a convex disc with smooth boundary where we have at most three topological discs as tiles. This result is a far-reaching generalization of the results of Kurusa, Lángi and Vígh \cite{KLV2020}. Some further partial results are proved for non-normal tilings.

22 pages, 15 figures