论文标题
$ l^2 $ - 扩展指数，更清晰的估算和曲率积极性
$L^2$-extension indices, sharper estimates and curvature positivity
论文作者
论文摘要
在本文中，我们介绍了$ l^2 $ - 扩展指数的新概念。该索引是一个函数，可在每个点上都相对于ohsawa-takegoshi-type扩展的$ l^2 $ estimute的最小常数。通过使用这个概念，我们提出了一种研究曲率阳性的新方法。我们证明，$ l^2 $ - 扩展的敏锐度与曲率的积极程度之间存在等效。还系统地给出了Sharper $ l^2 $延伸的新示例。作为应用程序，我们使用$ l^2 $延伸指数来研究prékopa型定理，并研究某个直接图像捆的阳性。我们还提供了多毛性和曲率平坦度的新特征。
In this paper, we introduce a new concept of $L^2$-extension indices. This index is a function that gives the minimum constant with respect to the $L^2$-estimate of an Ohsawa--Takegoshi-type extension at each point. By using this notion, we propose a new way to study the positivity of curvature. We prove that there is an equivalence between how sharp the $L^2$-extension is and how positive the curvature is. New examples of sharper $L^2$-extensions are also systematically given. As applications, we use the $L^2$-extension index to study Prékopa-type theorems and to study the positivity of a certain direct image sheaf. We also provide new characterizations of pluriharmonicity and curvature flatness.
