论文标题
沿曲率流的质量不平等现象的稳定性
Stability of quermassintegral inequalities along inverse curvature flows
论文作者
论文摘要
在本文中，我们考虑了沿反向曲率流的Quermassintegral不平等现象的稳定性。我们选择了流量的特殊重新缩放，以便$ k $ - QuermassIntegral正在减少，并保留了$ K-1 $ -Th QuermassIntegral。沿着这种重新恢复的流，我们证明$ k $ - QuermassIntegral的降低速度比域的Fraenkel不对称性快于接近球体时的速度快。这导致了使用流量方法的几乎球形组的Quermassintegral不等式的稳定性不等式。
In this paper, we consider the stability of quermassintegral inequalities along a inverse curvature flow. We choose a special rescaling of the flow such that the $k$-th quermassintegral is decreasing and the $k-1$-th quermassintegral is preserved. Along this rescaled flow, we prove that the decreasing rate of the $k$-th quermassintegral is faster than the Fraenkel asymmetry of the domain when approaching to the sphere. This leads to the stability inequality of quermassintegral inequalities for nearly spherical sets using the flow method.
