题目：The Reverse-Log-Brunn-Minkowski Inequality

报告人：席东盟 教授 （上海大学）

地点：致远楼101室

时间：2024年5月21日 9:00-10:00

摘要: 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, using the “reverse-to- forward 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 Handel). Via a study of the lemma of relations, the full equality conditions (“dilated direct summands”) are also characterized, which turns to be new.

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