Mixed volumes and the Bochner method
Mixed volumes and the Bochner method
复制标题
混合体积和博赫纳方法
DOI：
10.1090/proc/14651
复制
发表时间：
2019
影响因子：
1
通讯作者：
van Handel, Ramon
中科院分区：
文献类型：
--
作者：
Shenfeld, Yair;van Handel, Ramon
凸几何的核心在于观察凸体的体积表现为多项式。许多几何不等式可以用这个多项式的系数来表示，称为混合体积。这个理论最深刻的结果之一是亚历山德罗夫-芬切尔不等式，它包含了许多已知的不等式作为特殊情况。本文的目的是给出亚历山德罗夫-芬切尔不等式及其矩阵对应物--混合判别式的亚历山德罗夫不等式的新证明，这些证明在概念上和技术上都比以前的证明简单，并阐明了基本结构。我们的主要观察是，这些不等式可以减少的谱定理某些平凡的“Bochner公式”。引用
At the heart of convex geometry lies the observation that the volume of convex bodies behaves as a polynomial. Many geometric inequalities may be expressed in terms of the coefficients of this polynomial, called mixed volumes. Among the deepest results of this theory is the Alexandrov-Fenchel inequality, which subsumes many known inequalities as special cases. The aim of this note is to give new proofs of the Alexandrov-Fenchel inequality and of its matrix counterpart, Alexandrov’s inequality for mixed discriminants, that appear conceptually and technically simpler than earlier proofs and clarify the underlying structure. Our main observation is that these inequalities can be reduced by the spectral theorem to certain trivial “Bochner formulas”. References
关于混合判别式和体积的备注
影响因子：
1.6
作者：
S. Artstein;D. Florentin;Y. Ostrover
通讯作者：
Y. Ostrover