Interpolation in non-positively curved Kähler manifolds

Open problems on structure of positively curved projective varieties

We provide supplements and open problems related to structure theorems for maximal rationally connected fibrations of certain positively curved projective varieties, including smooth projective varieties with semi-positive holomorphic sectional curvature, pseudo-effective tangent bundle, and nef anti-canonical divisor.

Positively curved Finsler metrics on vector bundles

We construct a convex and strongly pseudoconvex Kobayashi positive Finsler metric on a vector bundle $E$ under the assumption that the symmetric power of the dual $S^kE^*$ has a Griffiths negative $L^2$-metric for some $k$. The proof relies on the negativity of direct image bundles and the Minkowski inequality for norms. As a corollary, we show that given a strongly pseudoconvex Kobayashi positive Finsler metric, one can upgrade to a \textit{convex} Finsler metric with the same property. We also give an extremal characterization of Kobayashi curvature for Finsler metrics.

向量丛上的正曲率芬斯勒度量 III

Positively curved Finsler metrics on vector bundles III

本文证明了小林正向量丛的商丛和张量积仍为小林正，从而加强了丰富性、格里菲斯正性与小林正性之间的猜想等价关系。

向量丛上的正曲率芬斯勒度量 II

Positively curved Finsler metrics on vector bundles II

该研究针对满足特定曲率界的丰富向量丛，通过比较高阶行列式与对称幂的曲率、利用凸芬斯勒度量对偶性，证明了相关向量丛的Kobayashi正性，并在附加条件下得到Griffiths正性结果。

完备非正曲率Kähler流形上第二主定理的精化形式

A refined form of the second main theorem on complete non-positively curved Kähler manifolds

针对一般非正曲率Kähler流形上第二主定理误差项难以优化的问题，基于A. Atsuji的工作，利用良好估计提出了亚纯映射第二主定理的精化形式，改进了2018年的误差项结果。

Miyaoka-Yau不等式中的等式与非正曲率klt对的均匀化

Equality in the Miyaoka-Yau inequality and uniformization of non-positively curved klt pairs

本文研究了紧Kähler klt对在orbifold Miyaoka-Yau不等式中等号成立的条件，证明了此时其orbifold泛覆盖为单位球或仿射空间。