The logarithmic Minkowski inequality for non-symmetric convex bodies |
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Affiliation: | Department of Mathematics and Statistics, Concordia University, Montreal, QC, H3G 1M8, Canada |
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Abstract: | We validate the conjectured logarithmic Minkowski inequality, and thus the equivalent logarithmic Brunn–Minkowski inequality, in some particular cases and we prove some variants of the logarithmic Minkowski inequality for general convex bodies without the symmetry assumption. An application of one of these variants is shown. |
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Keywords: | Cone-volume measure Log-Brunn–Minkowski inequality Log-Minkowski inequality |
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