论文标题
曲率估计和差距定理，用于扩展Ricci Soliton
Curvature estimates and gap theorems for expanding Ricci solitons
论文作者
论文摘要
我们为非平板和非压缩扩展梯度Ricci Soliton的标量曲率得出了尖锐的下限，前提是标量曲率是非负数的，并且潜在函数是正确的。当RICCI曲率是非阳性并且电势函数适当的情况下，我们还为非关系扩展器的标量曲率提供了上限。然后，我们为扩展孤子的标态曲率提供了足够的条件。我们还估计了在三个和四个方面扩展孤子的曲率。作为应用程序，我们证明了三维梯度扩展器上的差距定理。
We derive a sharp lower bound for the scalar curvature of non-flat and non-compact expanding gradient Ricci soliton provided that the scalar curvature is non-negative and the potential function is proper. We also give an upper bound for the scalar curvature of noncompact expander when the Ricci curvature is nonpositive and the potential function is proper. We then provide a sufficient condition for the scalar curvature of expanding soliton being nonnegative. We also estimate the curvature of expanding soliton in dimensions three and four. As an application, we prove a gap theorem on three dimensional gradient expander.
