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- W4384111101 abstract "Firstly, we propose our conjectured Reverse-log-Brunn-Minkowski inequality (RLBM). Secondly, we show that the (RLBM) conjecture is equivalent to the log-Brunn-Minkowski (LBM) conjecture proposed by Boroczky-Lutwak-Yang-Zhang. We name this as ``reverse-to-forward principle. Using this principle, we give a very simple new proof of the log-Brunn-Minkowski inequality in dimension two. Finally, we establish the ``reverse-to-forward principle for the log-Minkowski inequality (LM).Using this principle, we prove the log-Minkowski inequality in the case that one convex body is a zonoid (the inequality part was first proved by van Handle). Via a study of the lemma of relations, the full equality conditions (``dilated direct summands) are also characterized, which turns to be new." @default.
- W4384111101 created "2023-07-13" @default.
- W4384111101 creator A5037382354 @default.
- W4384111101 date "2023-07-09" @default.
- W4384111101 modified "2023-09-27" @default.
- W4384111101 title "The Reverse-log-Brunn-Minkowski inequality" @default.
- W4384111101 doi "https://doi.org/10.48550/arxiv.2307.04266" @default.
- W4384111101 hasPublicationYear "2023" @default.
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