发表机构
Goethe-Universität Frankfurt; CUNEF Universidad（法兰克福歌德大学; CUNEF大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文建立了一种广义Alexandrov-Fenchel不等式，通过放宽半正定条件并扩展Alexandrov不等式，推导出面积测度线性泛函的对数凹性和平均截面体内蕴体积的Brunn-Minkowski型不等式，解决了两个公开问题。
AI 中文摘要
我们建立了一种Alexandrov-Fenchel型不等式，其中参考体之一被一个其Hessian矩阵的特征值满足平衡条件（而不要求半正定）的函数所替代。证明依赖于对混合判别式的Alexandrov不等式的新扩展。作为应用，我们推导出面积测度的线性泛函的对数凹性原理，回答了Colesanti、Hug和Saorín-Gómez的问题，以及平均截面体的内蕴体积的Brunn-Minkowski型不等式，回答了Schuster的问题。
英文摘要
We establish an Alexandrov--Fenchel type inequality in which one of the reference bodies is replaced by a function whose Hessian satisfies a balancing condition on its eigenvalues, without being required to be positive semidefinite. The proof hinges on a new extension of Alexandrov's inequality for mixed discriminants. As applications, we derive a log-concavity principle for linear functionals of area measures, answering a question of Colesanti, Hug, and Saorín-Gómez, as well as Brunn--Minkowski type inequalities for intrinsic volumes of mean section bodies, answering a question of Schuster.
Comments29 pages
