2019/11/12 by K. J. Falconer, Falconer, Kenneth J., Jonathan M. Fraser +3
Computer Science · Engineering · #28A80 #Advanced Numerical Analysis Techniques #Digital Image Processing Techniques #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Packing Problems
paper · pdf · doi:10.48550/arxiv.1911.04857
openalex publication_date 2019/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present several applications of the Assouad dimension, and the related\nquasi-Assouad dimension and Assouad spectrum, to the box and packing dimensions\nof orthogonal projections of sets. For example, we show that if the\n(quasi-)Assouad dimension of F \⊆ rn is no greater than m, then the\nbox and packing dimensions of F are preserved under orthogonal projections\nonto almost all m-dimensional subspaces. We also show that the threshold m\nfor the (quasi-)Assouad dimension is sharp, and bound the dimension of the\nexceptional set of projections strictly away from the dimension of the\nGrassmannian.\n