论文标题
托里不能崩溃到一个间隔
Tori Can't Collapse to an Interval
论文作者
论文摘要
在这里，我们证明，在较低的部分曲率结合下，一系列riemannian歧管与标准的$ m $二维圆环无法在gromov-hausdorff sense中融合到封闭的间隔。 该证明是通过分析从burogo-gromov- yamaguchi纤维定理的perelman概括获得的矛盾序列的适当封面来完成的。
Here we prove that under a lower sectional curvature bound, a sequence of Riemannian manifolds diffeomorphic to the standard $m$-dimensional torus cannot converge in the Gromov--Hausdorff sense to a closed interval. The proof is done by contradiction by analyzing suitable covers of a contradicting sequence, obtained from the Burago--Gromov--Perelman generalization of the Yamaguchi fibration theorem.
