北京师范大学数学科学学院

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北京师范大学数学科学学院

2024-07-08 07:08| 来源: 网络整理| 查看: 265

[1] Zhiwei Wang, On the volume of a pseudo-effective class and semi-positive properties of the Harder-narasimhan filtration on a compact Hermitian manifold, Annales Polonici Mathematici, 117(2016), 41-58.主要结果:部分解决Boucksom猜想。[2] Zhiwei Wang and Xiangyu Zhou, CR eigenvalue estimate and Kohn-Rossi cohomology, J. Differential Geom., 126 (2024), 1207-1244.主要结果:得到一类弱拟凸CR流形的CR拉普拉斯算子的特征值的最优渐近估计。[3] Fusheng Deng, Zhiwei Wang, Liyou Zhang and Xiangyu Zhou, New characterization of plurisubharmonic functions and positivity of direct images, Amer. J. Math., 146, No. 3, June 2024,751-768. 主要结果:得到O-T延拓定理的逆,给出多次调和函数新刻画,并得到研究direct image的Griffiths正性的全新方法。[4] Fusheng Deng, Zhiwei Wang, Liyou Zhang and Xiangyu Zhou, Linear invariants of complex manifolds and their plurisubharmonic variations, J. Funct. Anal. 279, no.1, 108514.主要结果:首次建立高维非紧复流形的完备的线性不变量理论。被称为是“fundamental result”。[5] Fusheng Deng, Jiafu Ning and Zhiwei Wang, Characterizations of Plurisubharmonic functions, Sci. China Math. 64 (2021),no.9,1959--1970.主要结果:(对平凡线丛)系统建立L^2理论的逆理论的基本框架。[6] Fusheng Deng, Jiafu Ning, Zhiwei Wang and Xiangyu Zhou, Positivity of holomorphic vector bundles in terms of $L^p$-conditions of $\bar\partial$, Math. Ann. 385 (2023), no. 1-2, 575-607。主要结果:对向量丛系统建立L^2理论的逆理论;建立全纯向量丛Nakano正性的充要条件;建立研究direct image的Nakano正性的全新方法。[7] Jiafu Ning, Zhiwei Wang and Xiangyu Zhou, On the extension of Kaehler currents on compact Kaehler manifolds: holomorphic retraction case, arXiv:2105.08224. Accepted by Ann. Fac. Sci. Toulouse Math.主要结果:给出Coman-Guedj-Zeriahi问题的一个部分解答。[8] Xiankui Meng and Zhiwei Wang, A Kahlerness criterion for real (1,1)-classes on projective manifolds through extendibility of singular potentials. Sci. China Math., 65(9), 1795-1802, 2022.主要结果:利用奇异权的延拓条件给出射影流形上超越上同调类的属于凯勒类的一个判别法则。[9] Yinji Li, Zhiwei Wang and Xiangyu Zhou, Degenerate complex Monge-Amp\` ere type equations on compact Hermitian manifolds and applications, arXiv:2305.17955. Accepted by Transactions of the American Mathematical Society.主要结果:得到紧埃尔米特流形上一类退化蒙日-安培方程的解,作为应用部分解决Demailly-Paun猜想和Tosatti-Weinkove猜想。



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