Article: Minkowski Weak Embedding Theorem
My article Minkowski weak embedding theorem1 with Stathis Chrontsios-Garitsis just got accepted at HJM, so it’s high time that I write a short summary.
The two sentence version: The Assouad embedding theorem loosely states that any metric space with finite Assouad dimension can be embedded into $\mathbb{R}^n$ without too much distortion. The Minkowski (or box-counting) dimension is smaller than the Assouad dimension and we show that an analogue of the Assouad embedding theorem still holds if one replaces the assumption of finite Assouad dimension with the weaker assumption of finite Minkowski dimension.