论文标题
线束平均曲率流的稳定性
Stability of line bundle mean curvature flow
论文作者
论文摘要
令$（x，ω）$为复杂尺寸$ n $和$（l，h）$的紧凑型kähler歧管，为$ x $的全体形状线束。在\ cite {jy}中引入了线束平均曲率流，以便在$ l $上找到变形的Hermitian-yang-mills指标。在本文中，我们考虑了线束平均曲率流的稳定性。假设存在$ l $上的Hermitian Yang-Mills度量$ \ HAT h $。我们证明，只要初始指标接近$ c^2 $ -norm中的$ c^\ infty $ sense，$ c^\ infty $ sense的线束平均曲率流就$ c^\ infty $ sense呈指数收敛。
Let $(X,ω)$ be a compact Kähler manifold of complex dimension $n$ and $(L,h)$ be a holomorphic line bundle over $X$. The line bundle mean curvature flow was introduced in \cite{JY} in order to find deformed Hermitian-Yang-Mills metrics on $L$. In this paper, we consider the stability of the line bundle mean curvature flow. Suppose there exists a deformed Hermitian Yang-Mills metric $\hat h$ on $L$. We prove that the line bundle mean curvature flow converges to $\hat h$ exponentially in $C^\infty$ sense as long as the initial metric is close to $\hat h$ in $C^2$-norm.
