Preprint
Aug 2026
Symmetry-dependence in Rounding of a Convex Body
The symmetry measure of a convex body $S\subset\mathbb{R}^n$ is given by: $\mathrm{sym}(S):=\max\{\alpha\ge0:\text{ there exists }x\in S\text{ such that }-\alpha(S-x)\subseteq S-x\}$, where such an $x$ is called a Minkowski center. We prove that every convex body $S$ admits a $\sqrt{\frac{n}{\mathrm{sym}(S)}}$-rounding...
Zi-Kai Xiong, Robert M. Freund
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