论文标题
凸影域中距离之间的最佳不平等现象
Optimal inequalities between distances in convex projective domains
论文作者
论文摘要
在实际投影空间中的任何适当凸面上，都存在天然的riemannian指标，即蓝施克度量。另一方面，可以在希尔伯特度量标准中测量点之间的距离。使用最佳控制技术，我们提供了不平等的线条段的riemannian长度，通过这些点之间的希尔伯特距离连接了两个点，从而增强了托洛赞的结果。我们的估计值适用于在凸投射域上的整个Riemannian指标，即凸出非分类质心含量浸入式浸入率的凸出域。如果浸入渐近渐近地上是在域上凸锥的边界，那么我们还可以上限riemmanian长度。在这些类别，尤其是对于Blaschke指标上，我们的不平等是最佳的。
On any proper convex domain in real projective space there exists a natural Riemannian metric, the Blaschke metric. On the other hand, distances between points can be measured in the Hilbert metric. Using techniques of optimal control, we provide inequalities lower bounding the Riemannian length of the line segment joining two points of the domain by the Hilbert distance between these points, thus strengthening a result of Tholozan. Our estimates are valid for a whole class of Riemannian metrics on convex projective domains, namely those induced by convex non-degenerate centro-affine hypersurface immersions. If the immersions are asymptotic to the boundary of the convex cone over the domain, then we can also upper bound the Riemmanian length. On these classes, and in particular for the Blaschke metric, our inequalities are optimal.
