论文标题
圆环不能崩溃到一段
Torus cannot collapse to a segment
论文作者
论文摘要
在较早的工作中，我们分析了在高斯曲率下的下限的条件下，不可能通过负欧拉特征的表面崩溃。在这里，我们表明，在类似的条件下，圆环无法崩溃到一个细分市场。与圆环不同，克莱因瓶可以崩溃到一个细分市场。我们表明，在这种情况下，同源性的循环必须保持统一的距离。
In earlier work, we analyzed the impossibility of codimension-one collapse for surfaces of negative Euler characteristic under the condition of a lower bound for the Gaussian curvature. Here we show that, under similar conditions, the torus cannot collapse to a segment. Unlike the torus, the Klein bottle can collapse to a segment; we show that in such a situation, the loops in a short basis for homology must stay a uniform distance apart.
