A characterization of semisimple local system by tame pure imaginary pluri-harmonic metric

平衡和多调和度量在实半单李群上的应用

Balanced and pluriclosed metrics on real semisimple Lie groups

研究实半单李群的紧致商在正则复结构下平衡和多调和度量的存在性，通过Vogan图分类，并指出此类复流形不能同时拥有这两种度量。

紧半单李群上的多值闭合度量

Pluriclosed metrics on compact semisimple Lie groups

研究紧半单李群上左和Ad(T)-不变的多值闭合度量，揭示其与CYT度量的关系及多值闭合流的性质。

Real semisimple Lie groups and balanced metrics

Given any non-compact real simple Lie group G of inner type and even dimension, we prove the existence of an invariant complex structure J and a Hermitian balanced metric with vanishing Chern scalar curvature on G and on any compact quotient $M=G/Γ$, with $Γ$ a cocompact lattice. We also prove that (M,J) does not carry any pluriclosed metric, in contrast to the case of even dimensional compact Lie groups, which admit pluriclosed but not balanced metrics.

Asymptotic behaviour of tame nilpotent harmonic bundles with trivial parabolic structure

Let $E$ be a holomorphic vector bundle. Let $θ$ be a Higgs field, that is a holomorphic section of $End(E)\otimesΩ^{1,0}_X$ satisfying $θ^2=0$. Let $h$ be a pluriharmonic metric of the Higgs bundle $(E,θ)$. The tuple $(E,θ,h)$ is called a harmonic bundle. Let $X$ be a complex manifold, and $D$ be a normal crossing divisor of $X$. In this paper, we study the harmonic bundle $(E,θ,h)$ over $X-D$. We regard $D$ as the singularity of $(E,θ,h)$, and we are particularly interested in the asymptotic behaviour of the harmonic bundle around $D$. We will see that it is similar to the asymptotic behaviou…

Asymptotic behaviour of tame harmonic bundles and an application to pure twistor $D$-modules

We study the asymptotic behaviour of tame harmonic bundles. First of all, we prove a local freeness of the prolongation by an increasing order. Then we obtain the polarized mixed twistor structure. As one of the applications, we obtain the norm estimate of holomorphic or flat sections by weight filtrations of the monodromies. As other application, we establish the correspondence of semisimple regular holonomic $D$-modules and polarizable pure imaginary pure twistor $D$-modules through a tame pure imaginary harmonic bundles, which is a conjecture of Sabbah. Then the regular holonomic version of…

到建筑的多重调和映射与对称微分

Pluriharmonic maps into buildings and symmetric differentials

本研究将Gromov-Schoen的多重调和映射构造推广到复光滑拟射影簇情形，构造了到Bruhat-Tits建筑的等变多重调和映射，并借此将Brunebarbe等人关于整体对数对称微分非零性的结论推广到拟射影情形。