Brunn-Minkowski type inequalities for the lattice point enumerator
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DOI: 10.1016/j.aim.2020.107193
Abstract: Geometric and functional Brunn-Minkowski type inequalities for the lattice point enumerator $\mathrm{G}_n(\cdot)$ are provided. In particular, we show that $$\mathrm{G}_n((1-\lambda)K + \lambda L + (-1,1)^n)^{1/n}\geq (1-\lambda)\mathrm{G}_n(K)^{1/n}+\lambda\mathrm{G}_n(L)^{1/n}$$ for any non-empty bounded sets $K, L\subset\mathbb{R}^n$ and all… read more here.
Keywords: brunn minkowski; type inequalities; lattice point; lambda ... See more keywords