标题： 正性与$\mathbf{L^2}$扩展 显示英文标题

标题： Positivity and $\mathbf{L^2}$ Extension

摘要： 我们考察向量丛 E 的正性与高阶全纯 E-值微分形式的$L^2$扩展问题之间的关系。 特别地，我们通过例子说明 Griffiths 正性是不够的。 尽管 Nakano 正性对于 E 的充分性早已为人所知，但我们沿着 Berndtsson 和 Lempert 的思路提供了另一种证明。 为了这种证明，我们建立了一个向量丛的类似 Berndtsson 一个著名结果的结论。 这个结果具有独立的兴趣，并应有许多其他有用的应用。 显示英文摘要

摘要： We examine the relationship between positivity of a vector bundle E and the problem of $L^2$ extension of holomorphic E-valued forms of top degree. In particular, we show by example that Griffiths positivity is not enough. Though the sufficiency of Nakano positivity of E has been known for some time, we provide another proof along the lines of Berndtsson and Lempert. For such a proof we establish a vector bundle analogue of a well-known result of Berndtsson. This result is of independent interest and should have many other useful applications.