3 problems

Let $X\subset\mathbb{R}^n$ be compact and convex, and let $\mathcal{M}_X(R):=\operatorname{mag}(X,R\cdot\mathrm{d})$ for $R>0$. For $0\leq k\leq n$, let $V_k(X)$ denote the intrins…

Let $X$ be a compact subspace of Euclidean space for which alpha magnitude dimension is defined. The alpha magnitude dimension conjecture. Alpha magnitude dimension is equivalent t…

For a convex subset $A$ of the plane, let $|A|$ denote its magnitude, let $\chi(A)$ denote its Euler characteristic, and let $p$ and $a$ denote its perimeter and area, respectively…