论文标题
Hermitian矢量束的不变直接图像的曲率积极性
Curvature positivity of invariant direct images of Hermitian vector bundles
论文作者
论文摘要
我们证明，关于满足某些条件的紧凑型组动作的不变部分，即在有界的pseudoconvex域上Nakano阳性Hermitian Holomorphic Vector Bundle的直接图像是Nakano的阳性。我们还考虑了非2级$ \ mathbb {r}^m $的动作，并为一个管域家族获得相同的结果，这为矩阵值prekopa的定理带来了一种新方法，最初由raufi证明。我们方法中的两种主要成分是Hörmander的$ l^2 $ $ \ bar \ partial $的理论，以及邓宁宁 - Zhang-Zhou最近的作品在表征Hermitian Holmitian Holomorphic Vector Bundles中Nakano阳性的表征。
We prove that the invariant part, with respect to a compact group action satisfying certain condition, of the direct image of a Nakano positive Hermitian holomorphic vector bundle over a bounded pseudoconvex domain is Nakano positive. We also consider the action of the noncompact group $\mathbb{R}^m$ and get the same result for a family of tube domains, which leads to a new method to the matrix-valued Prekopa's theorem originally proved by Raufi. The two main ingredients in our method are Hörmander's $L^2$ theory of $\bar\partial$ and the recent work of Deng-Ning-Zhang-Zhou on characterization of Nakano positivity of Hermitian holomorphic vector bundles.
