论文标题
最大度量的较高维差距定理
Higher dimensional gap theorems for the maximum metric
论文作者
论文摘要
最近，第一作者与Jens Marklof一起研究了经典的三个距离定理对较高尺寸旋转的概括，相对于任何平坦的Riemannian度量，在相应距离数量的所有维度上给出了上限。在第二个维度中，他们证明了五个距离定理，这是最好的。在本文中，我们在所有维度上建立了类似的界限，以实现最大度量。我们还表明，在两个和三个方面，我们的界限是最好的。
Recently, the first author together with Jens Marklof studied generalizations of the classical three distance theorem to higher dimensional toral rotations, giving upper bounds in all dimensions for the corresponding numbers of distances with respect to any flat Riemannian metric. In dimension two they proved a five distance theorem, which is best possible. In this paper we establish analogous bounds, in all dimensions, for the maximum metric. We also show that in dimensions two and three our bounds are best possible.
