论文标题
部分可观测时空混沌系统的无模型预测
On the volume of the Minkowski sum of zonoids
论文作者
论文摘要
我们探索限制在派系类别的凸几何形状中的一些不等式。我们显示了在众多的宗教团体中，在局部Alexandrov-fenchel不平等，局部Loomis-Whitney不平等，体积的对数 - 模块化和Dembo-Cover-Thomas cosienture of Voluge与表面积的比率的单调性。除这些等价外，我们还以$ {\ Mathbb r}^3 $确认这些猜想，并在$ {\ Mathbb r^2} $中建立了改进的不平等。在此过程中，我们对亚当·马库斯（Adam Marcus）的问题给出了否定的答案，该问题涉及斯坦纳（Steiner）多项式的根源。我们还研究了$ L_P $ -BRUNN-MINKOWSKI理论中的类似问题，尤其是，我们在任何维度上确认了上述所有猜想$ p = 2 $。
We explore some inequalities in convex geometry restricted to the class of zonoids. We show the equivalence, in the class of zonoids, between a local Alexandrov-Fenchel inequality, a local Loomis-Whitney inequality, the log-submodularity of volume, and the Dembo-Cover-Thomas conjecture on the monotonicity of the ratio of volume to the surface area. In addition to these equivalences, we confirm these conjectures in ${\mathbb R}^3$ and we establish an improved inequality in ${\mathbb R^2}$. Along the way, we give a negative answer to a question of Adam Marcus regarding the roots of the Steiner polynomial of zonoids. We also investigate analogous questions in the $L_p$-Brunn-Minkowski theory, and in particular, we confirm all of the above conjectures in the case $p=2$, in any dimension.
