NOTES ON THE LOG-BRUNN-MINKOWSKI INEQUALITY*

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doi:10.1007/s10473-023-0601-x

Abstract: Böröczky-Lutwak-Yang-Zhang proved the log-Brunn-Minkowski inequality for two origin-symmetric convex bodies in the plane in a way that is stronger than for the classical Brunn-Minkowski inequality. In this paper, we investigate the relative positive center set of planar convex bodies. As an application of the relative positive center, we prove the log-Minkowski inequality and the log-Brunn-Minkowski inequality.

Key words: cone-volume measure, dilation position, log-Brunn-Minkowski's inequality, log-Minkowski's inequality, relative positive center

CLC Number:

52A40

Yunlong YANG, Nan JIANG, Deyan ZHANG. NOTES ON THE LOG-BRUNN-MINKOWSKI INEQUALITY^*[J].Acta mathematica scientia,Series B, 2023, 43(6): 2333-2346.

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