2017/11/17 by Yu, Han
#05B30 #28A78 #52C17 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.1711.06544
In this paper we study some cube packing problems. In particular we are interested in compact subsets of ℝn,n≥ 2, which contain boundaries of cubes with all side lengths in (0,1). We show here that such sets must have lower box dimension at least n-0.5 and we will also provide sharp examples. We also show here that such sets must be large in general in a precise sense which is also introduced in this paper.