Philip Gibbs (2019). An Upper Bound for Lebesgue’s Covering Problem. RESEARCHERS.ONE, https://www.researchers.one/article/2019-08-23.

A covering problem posed by Henri Lebesgue in 1914 seeks to find the convex shape of smallest area that contains a subset congruent to any point set of unit diameter in the Euclidean plane. Methods used previously to construct such a covering can be refined and extended to provide an improved upper bound for the optimal area. An upper bound of 0.8440935944 is found.