论文标题
标量曲率在尺寸四的极端和刚度
Extremality and rigidity for scalar curvature in dimension four
论文作者
论文摘要
在Gromov之后，如果任何增加标量曲率的修改必须减少某些切线2平面的面积，则称为区域歧管。我们证明，具有或没有边界的大量紧凑型4个manifolds具有非负截面曲率是面积 - 超级曲率。我们还表明，在4个manifolds上的所有正截面曲率区域都是局部面积的。这些结果是在分析曲折操作员的内核中分析的部分，该部分是由成对度量的构造的，并使用Finsler-Thorpe-Thorpe Trick在维度4中进行截面曲率边界。
Following Gromov, a Riemannian manifold is called area-extremal if any modification that increases scalar curvature must decrease the area of some tangent 2-plane. We prove that large classes of compact 4-manifolds, with or without boundary, with nonnegative sectional curvature are area-extremal. We also show that all regions of positive sectional curvature on 4-manifolds are locally area-extremal. These results are obtained analyzing sections in the kernel of a twisted Dirac operator constructed from pairs of metrics, and using the Finsler--Thorpe trick for sectional curvature bounds in dimension 4.
