论文标题
QuermassIntegral保留球中的平均曲率流
The quermassintegral preserving mean curvature flow in the sphere
论文作者
论文摘要
我们引入了一个平均曲率流，并在球体中具有凸超曲面的全局项，为此，可以选择全局项以保持任何QuermassIntegral固定。然后，从严格凸出的初始hyperface开始，我们证明该流量存在于所有时间，并顺利收敛到地理球体。这为Huisken在1987年引入的球体中存在的问题中存在的问题提供了解决方法。我们还为某些恒定的曲率方程式在空间形式以及球体和DE Sitter空间的上分支中的孤子方程式进行了分类。
We introduce a mean curvature flow with global term of convex hypersurfaces in the sphere, for which the global term can be chosen to keep any quermassintegral fixed. Then, starting from a strictly convex initial hypersurface, we prove that the flow exists for all times and converges smoothly to a geodesic sphere. This provides a workaround to an issue present in the volume preserving mean curvature flow in the sphere introduced by Huisken in 1987. We also classify solutions for some constant curvature type equations in space forms, as well as solitons in the sphere and in the upper branch of the De Sitter space.
