论文标题
$ l^2 $ - 最小的延伸范围超过了赫尔米尼对称域
$L^2$-minimal extensions over Hermitian symmetric domains
论文作者
论文摘要
在本文中，我们研究了hodge结构的极化变化与Hermitian对称域的极化变化的$ l^2 $ - 最小扩展问题。我们能够使用集体理论结构明确地找到$ l^2 $ - 最小的扩展。特别是，这提供了一个构造，而无需使用$ l^2 $估计，如Ohsawa-Takegoshi型扩展定理。关键成分是Harish-Chandra嵌入了Hermitian对称域。 全体形态部分的构建可能具有独立的兴趣，因为它在Hermitian VHS的环境中提供了具体的描述。
In this paper, we study the $L^2$-minimal extension problem for polarized variations of Hodge structures over Hermitian symmetric domains. We are able to explicitly find the $L^2$-minimal extensions using a group-theoretic construction. In particular, this gives a construction without using $L^2$-estimates as in the Ohsawa-Takegoshi type extension theorems. The key ingredient is the Harish-Chandra embedding of Hermitian symmetric domains. The construction of holomorphic sections might be of independent interest since it gives a concrete description in the setting of Hermitian VHS.
