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- W4281738140 abstract "We explore some inequalities in convex geometry restricted to the class of zonoids. We show the equivalence, in the class of zonoids, between a local Alexandrov-Fenchel inequality, a local Loomis-Whitney inequality, the log-submodularity of volume, and the Dembo-Cover-Thomas conjecture on the monotonicity of the ratio of volume to the surface area. In addition to these equivalences, we confirm these conjectures in ${mathbb R}^3$ and we establish an improved inequality in ${mathbb R^2}$. Along the way, we give a negative answer to a question of Adam Marcus regarding the roots of the Steiner polynomial of zonoids. We also investigate analogous questions in the $L_p$-Brunn-Minkowski theory, and in particular, we confirm all of the above conjectures in the case $p=2$, in any dimension." @default.
- W4281738140 created "2022-06-13" @default.
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- W4281738140 date "2022-06-05" @default.
- W4281738140 modified "2023-10-16" @default.
- W4281738140 title "On the volume of the Minkowski sum of zonoids" @default.
- W4281738140 doi "https://doi.org/10.48550/arxiv.2206.02123" @default.
- W4281738140 hasPublicationYear "2022" @default.
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