发表机构
Fudan University; Shanghai Center for Mathematical Sciences; Tongji University（复旦大学; 上海数学中心; 同济大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明了中心凸体的对数Brunn--Minkowski和对数Minkowski不等式，刻画了锥体积测度相同的条件，并推广到L_p情形，建立了表面积测度的唯一性。
AI 中文摘要
对于质心位于原点的凸体，证明了其对数Brunn--Minkowski和对数Minkowski不等式成立，等号成立当且仅当这些凸体是共同直接和项的正向独立膨胀。这刻画了中心凸体何时具有相同的锥体积测度。此外，对于每个p>0，还获得了L_p Brunn--Minkowski和Minkowski不等式，等号仅在正膨胀时成立，并建立了中心L_p表面积测度的相应唯一性。
英文摘要
The logarithmic Brunn--Minkowski and logarithmic Minkowski inequalities are proved for convex bodies whose centroids are at the origin, with equality precisely for independent positive dilations of common direct summands. This characterizes when centered convex bodies have the same cone-volume measure. The \(L_p\) Brunn--Minkowski and Minkowski inequalities are also obtained for every \(p>0\), with equality only for positive dilates, and the corresponding uniqueness of centered \(L_p\) surface area measures is established.
Comments33 pages
