2020-present, Assistant Professor, ShanghaiTech University
2016—2017, ERC program in Kähler and Algebraic geometry, Mathematics, Fourier Institute
2014-2016 Britton Postdoctoral Fellows, Mathematics, McMaster University
2008-2014 Ph.D. Mathematics, Stony Brook University
2005-2008 B.S. Mathematics and Physics, Hong Kong University
My main interest is in Complex geometry and Complex analysis. In particular, the core of my work is on uniqueness and existence of singular extremal metrics on Kähler manifolds. These questions are very classical Geometric Analysis problems at the ﬁrst glance. However, the attractive point is that many diﬀerent areas are actually related to them. For instance, the convexity of the so called Mabuchi functional, which is very useful from the view of the Variational Methods, is heavily related to topics in Kähler geometry, Several Complex Variables and Pluripotential Theory. Another example is the study of the conic extremal Kähler metrics, and this in fact investigates certain algebraic structures (orbiford singularities) on Kähler manifolds. Moreover, from the quantization point of view, the study of Donaldson’s balanced metrics, which is a ﬁnite dimensional version of the extremal metrics, is quite related to the philosophy of Symplectic Geometry.
1. Long Li, Strict convexity of the Mabuchi functional along energy minimizers. arXiv:1711.09717
2. Bo Li, Long Li, Bin Xu, Hyperbolic metrics and bounded projective functions with isolated singularities. arXiv:1709.03112
3. Long Li, Regularization of plurisubharmonic functions with a net of good points. arXiv:1705.07315
4. Long Li, Kai Zheng, Uniqueness of constant scalar curvature Kähler metrics with cone singularities, I: Reductivity. arXiv:1603.01743, To appear in Math. Ann.
5. Long Li, Subharmonicity of conic Mabuchi’s functional, I. arXiv:1511.00178, To appear in Annales de l’Institut Fourier
6. Long Li, Kai Zheng, A continuity method approach to uniqueness of Kähler-Einstein cone metrics. arXiv: 1511.02410, to appear in Calcu lus of Variations and Partial Diﬀerential Equations
7. Xiuxiong Chen, Long Li, Mihai Păun, Approximation of weak geodesics and subharmonicity of Mabuchi energy. Les Annales de la Faculte des Sciences de Toulouse.
8. Long Li, On the uniqueness of conical Kähler-Einstein metrics. arXiv 1402.4049
Long Li, On the Spectrum of weighted Laplacian operator and its application to uniqueness of Kähler Einstein metrics. Mathematische Annalen, August 2015, Volume 362, Issue 3, pp 1349-1378.