论文标题
球体中平均曲率流的尖锐捏合估计值
Sharp pinching estimates for mean curvature flow in the sphere
论文作者
论文摘要
我们证明了一套渐近尖锐的二次弯曲曲率捏合估计值的平均曲率流，这将Simons的刚性定理推广到最小的超曲面。然后，我们获得了第二种基本形式的衍生估计，我们通过紧凑的论点使用该估计来获得凸度估计。共同的凸度和圆柱估计产生了奇异模型的部分分类。我们还为古代解决方案获得了新的刚性结果。
We prove a suite of asymptotically sharp quadratic curvature pinching estimates for mean curvature flow in the sphere which generalize Simons' rigidity theorem for minimal hypersurfaces. We then obtain derivative estimates for the second fundamental form which we utilize, via a compactness argument, to obtain a convexity estimate. Together, the convexity and cylindrical estimates yield a partial classification of singularity models. We also obtain new rigidity results for ancient solutions.
