论文标题
一个人可以在平均曲率较大的球体上扰动赤道区吗？
Can One Perturb the Equatorial Zone on a Sphere with Larger Mean Curvature?
论文作者
论文摘要
我们考虑赤道区域上赤道区域的平均曲率刚度问题，该球体对赤道的对称，宽度为2 $ 2W $。关于刚性有两个不同的概念，即强刚度和局部刚性。我们证明，对于每种这些刚性问题，存在一个临界值，因此，只有当区域宽度小于该值时，刚性才能成立。对于刚性部分，我们使用了切线原理和特定的引理（我们之前建立的陷阱片诱饵）。对于非依据部分，我们通过使用Delaunay表面的称为圆角引理的胶合过程来构建非平凡的扰动。
We consider the mean curvature rigidity problem of an equatorial zone on a sphere which is symmetric about the equator with width $2w$. There are two different notions on rigidity, i.e. strong rigidity and local rigidity. We prove that for each kind of these rigidity problems, there exists a critical value such that the rigidity holds true if, and only if, the zone width is smaller than that value. For the rigidity part, we used the tangency principle and a specific lemma (the trap-slice lemma we established before). For the non-rigidity part, we construct the nontrivial perturbations by a gluing procedure called the round-corner lemma using the Delaunay surfaces.
