论文标题
高曲率高能量的非制作凸式凸式凸旧解决方案
Non-homothetic convex ancient solutions for flows by high powers of curvature
论文作者
论文摘要
我们证明存在封闭的古代解决方案，这些解决方案对于曲率流，对于大型负时，它们变得越来越椭圆形。速度函数是主曲线的一般对称函数，该度的均质大于一个。这概括了先前的曲率流量和其他单均匀曲率流的工作。作为辅助结果，我们证明了关于汇聚到凸旋转点的旋转点的新定理，可以满足曲线的适当约束。
We prove the existence of closed convex ancient solutions to curvature flows which become more and more oval for large negative times. The speed function is a general symmetric function of the principal curvatures, homogeneous of degree greater than one. This generalises previous work on the mean curvature flow and other one-homogeneous curvature flows. As an auxiliary result, we prove a new theorem on the convergence to a round point of convex rotationally symmetric hypersurfaces satisfying a suitable constraint on the curvatures.
