论文标题
Viterbo的猜想是蠕虫问题
Viterbo's conjecture as a worm problem
论文作者
论文摘要
在本文中，我们将Viterbo的猜想从象征性的几何形状到蠕虫问题的Minkowski版本，这是受到众所周知的Moser Worm Warress Insuper的启发。对于Lagrangian产品的特殊情况，这种关系提供了与收缩的Minkowski台球不平等和Mahler从凸几何形状的猜想的联系。此外，我们使用上述关系将Viterbo的猜想转移到了长期以来的开放式Wetzel问题的猜想中，这也可以作为收缩期欧几里得台球不平等表示，我们讨论一种算法方法，以便找到一种新的下限。最后，我们指出，维特尔博的猜想与Minkowski蠕虫问题之间的上述关系与Bellmann丢失的森林问题与原始Moser蠕虫问题之间的已知关系具有结构相似性。
In this paper, we relate Viterbo's conjecture from symplectic geometry to Minkowski versions of worm problems which are inspired by the well-known Moser worm problem from geometry. For the special case of Lagrangian products this relation provides a connection to systolic Minkowski billiard inequalities and Mahler's conjecture from convex geometry. Moreover, we use the above relation in order to transfer Viterbo's conjecture to a conjecture for the longstanding open Wetzel problem which also can be expressed as a systolic Euclidean billiard inequality and for which we discuss an algorithmic approach in order to find a new lower bound. Finally, we point out that the above mentioned relation between Viterbo's conjecture and Minkowski worm problems has a structural similarity to the known relationship between Bellmann's lost-in-a-forest problem and the original Moser worm problem.
