| 摘要: |
| 引入对数凹函数熵的Busemann-Petty问题,即对于2个Rn上的偶的对数凹函数f和g, 且f和g具有正的、有限的积分,假设∫Rn∩Hf(x)dx≤Rn∩Hg(x)dx对于任意i维子空间H均成立,是否能够得到Ent(f)≥Ent(g).得到了该问题的部分解答, 为解决凸体上的低维Busemann-Petty问题提供了一种新的途径. |
| 关键词: 低维Busemann-Petty问题 对数凹函数 i-相交体 i-相交函数 熵函数 |
| DOI：10.3969/J.ISSN.1000-5137.2023.03.004 |
| 分类号:O186.5 |
| 基金项目: |
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| The lower dimensional Busemann-Petty problem on entropy of log-concave functions |
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MA Dan, WANG Yalong
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Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China
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| Abstract: |
| In this paper, we introduce the lower dimensional Busemann-Petty problem on the entropy of log-concave functions: for two even log-concave functions f and g with positive and finite integrals in Rn, if ∫Rn∩Hf(x)dx is smaller than Rn∩Hg(x)dx for every i-dimensional subspace H, whether the entropy of f is larger than the entropy of g? Furthermore, partial answers to this problem are given, which might provide a new path to study the long-standing lower dimensional Busemann-Petty problem on convex bodies. |
| Key words: lower dimensional Busemann-Petty problem log-concave functions i-intersection bodies i-intersection functions entropy |
