超曲面的宏观稳定性与单纯范数
Macroscopic stability and simplicial norms of hypersurfaces
摘要：
我们引入了一个$\mathbb{Z}$ -系数版本的Guth的宏观稳定性不等式几乎极小化超曲面。在宏观数量曲率有下界的流形中，利用不等式证明了超曲面面积的一个下界，该下界是由超曲面的同调类的Gromov单纯范数表示的.我们给出的例子表明，一个非常积极的宏观数量曲率的下界并不一定意味着一个上界的面积极小化超曲面。
英文摘要：
We introduce a $\mathbb{Z}$--coefficient version of Guth's macroscopic stability inequality for almost-minimizing hypersurfaces. In manifolds with a lower bound on macroscopic scalar curvature, we use the inequality to prove a lower bound on areas of hypersurfaces in terms of the Gromov simplicial norm of their homology classes. We give examples to show that a very positive lower bound on macroscopic scalar curvature does not necessarily imply an upper bound on the areas of minimizing hypersurfaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
