Yi Li

Bio

Yi Li is a Professor of Mathematics at Southeast University and Shing-Tung Yau Center of Southeast University. He obtained his Ph.D in mathematics at Harvard in 2012.

Professor Li’s research interests include differential geometry, complex geometry, geometric analysis, geometric flow, nonlinear geometric type PDEs, general relativity. He has published over 25 papers in leading journals.

Education Experience

• 2007-2012    Harvard University    Pure Mathematics     PhD
• 2004-2007    Zhejiang University    Pure Mathematics     Master
• 2000-2004    Ningbo University    Pure Mathematics     Bachelor

Work Experience

• 2024-            SIMIS    Adjunct Professor
• 2019-            Southeast University and Yau Center of Southeast University    Professor
• 2016-2018    Universite du Luxembourg    Assistant-Chercheur
• 2013-2016    Shanghai JiaoTong University    Special Associate Researcher
• 2012-2013    Johns Hopkins University    Lecturer

Honors and Awards

1. 2016 Shanghai Jiao Tong University Teaching Achievement Grand Prize, with Liang Jin, Zhu Zuonong and Li Weimin.
2. 3rd Prize, Teaching Competition for Young Teachers in Shanghai Jiao Tong University, 2016

Publication (In preparation)

1. Li, Yi. CR twistor space and exceptional Lie groups, 2023.
2. Li, Yi. A project on Einstein scalar field equations.
3. Li, Yi. Geometry on Ricc-harmonic metrics.
4. Li, Yi; Yuan, Yuan. On a new geometric flow over Kahler manifolds III: long time behavior, in preparation, 2021.

Publication

1. Li, Yi; Zhang, Qianwei. Existence of solutions to a class of Kazdan-Warner equations on finite graphs, preprint, arXiv: 2308.10002, 2023 (submitted)
2. Li, Yi. Curvature pinching estimate under the Laplacian G_2 flow, preprint, arXiv: 2307.14289, 2023 (submitted)
3. Li, Yi. Curvature estimates on a parabolic flow of Fei-Guo-Phong, preprint, arXiv: 2210.16842, 2022 (submitted)
4. Li, Yi. A new notion on weighted Riemann curvature, Rendiconti del Circolo Matematico di Palermo Series 2, 2023.
5. Li, Yi; Li, Chuanhuan; Xu, Kairui. Parabolic frequency monotonicity on Ricci flow and Ricci-harmonic flow with bounded curvatures, The Journal of Geometric Analysis, 33, 282 (2023).
6. Li, Yi; Li, Chuanhuan. List’s flow with bounded integral curvature on noncompact complete Riemannian manifolds, preprint, 2022
7. Li, Yi; Zhang, Miaosen. A local curvature estimate for the Ricci-harmonic flow on complete Riemannian manifolds, preprint, http://arxiv.org/abs/2112.02576 (submitted)
8. Li, Yi. Local curvature estimates for the Ricci-harmonic flow, Nonlinear Analysis, 222(2022), No. 112961, 53pp.
9. Li, Yi; Yuan, Yuan. Local curvature estimates along the k-LYZ flow, J. Geom. Phys., 164(2021), 104162, 21pp.
10. Li, Yi. Local curvature estimates for the Laplacian flow, Cal. Var. PDE., 60(2021), no. 1, Paper No. 28, 37pp.
11. Li, Yi; Yuan, Yuan; Zhang, Yuguang. On a new geometric flow over Kahler manifolds, Comm. Analysis and Geometry, 28(2020), no. 6, 1251-1288.
12. Zhu, Xiaorui; Li, Yi. Harnack estimates for a heat-type equation under the geometric flow, Potential Analysis, 52(2020), 469-496. MR4067300
13. Li, Yi. Generalized Ricci flow II: existence for noncompact complete manifolds, Differential Geometry and its Applications, 66(2019), 106-154. MR3913713
14. Li, Yi. Scalar curvature along the Ricci flow, preprint, 2019 (submitted).
15. Li, Xiangdong; Li, Songzi; Li, Yi. Uniqueness and local curvature estimates for a class of generalized Ricci flow, preprint, 2019.
16. Li, Yi. Long time existence and bounded scalar curvature in the Ricci-harmonic flow, J. Differential Equations, 265(2018), no. 1, 69-97. MR3782539
17. Li, Yi; Zhu, Xiaorui. Harnack estimates for a nonlinear equation under Ricci flow, Differential Geometry and its Applications, 56(2018), 67-80. MR3759353
18. Wu, Guoqiang; Li, Yi. Heat kernel estimates along the Ricci-harmonic flow, preprint, 2017 (submitted)
19. Li, Yi. Long time existence of Ricci-harmonic flow, Front. Math. China, 11(2016), no. 5, 1313-1334. MR3547931
20. Li, Yi; Zhu, Xiaorui. Harnack estimates for a heat-type equation under the Ricci flow, J. Differential Equations, 260(2016), no. 4, 3270-3301. MR343499
21. Li, Yi. Li-Yau-Hamilton estimates and Bakry-Emery Ricci curvature, Nonlinear Anal., 113(2015), 1-32. MR3281843
22. Li, Yi; Liu, Kefeng. A geometric heat flow for vector fields, Sci. China Math., 58(2015), no. 4, 673-688.MR3319305
23. Zhu, Xiaorui; Li, Yi.Li-Yau estimates for a nonlinear parabolic equation on manifolds,Math. Phys. Anal. Geom., 17(2014), no. 3-4, 273-288. MR3291929
24. Li, Yi. A priori estimates for Donaldson’s equation over compact Hermitian manifolds, Cal. Var. PDE., 50(2014), no. 3-4, 867-882. MR3216837
25. Li, Yi. On an extension of the Hk-mean curvature flow for closed convex hypersurfaces, Geom. edicata,172(2014), 147-154. MR3253775
26. Li, Yi. Eigenvalues and entropies under the harmonic-Ricci flow, Pacific J. Math.,267 (2014), no. 1, 141-184. MR3163480
27. Li, Yi. Mabuchi and Aubin-Yau functionals over complex surfaces, J. Math. Anal. Appl., 416(2014), no. 1, 81-98. MR3182749
28. Li Yi. On an extension of the Hk-mean curvature flow, Sci. China Math., 55(2012), no. 1, 99-118. MR2873806
29. Li, Yi. Generalized Ricci flow I: higher derivatives estimates for compact manifolds, Analysis & PDE, 5(2012), no. 4, 747-775. MR3006641
30. Li, Yi. Mabuchi and Aubin-Yau functionals over complex manifolds, arXiv: 1004.0553, preprint.
31. Li, Yi. Mabuchi and Aubin-Yau functionals over complex three-folds, arXiv: 1003.5307, preprint.
32. Li Yi. Harnack inequality for the negative power Gaussian curvature flow, Proc. Amer. Math. Soc., 139(2011), no. 10, 3707-3717. MR2813400 (2012g: 53137)
33. Chen Lin; Li Yi; Liu Kefeng. Localization, Hurwitz numbers and the Witten conjecture, Asian J. Math., 12(2008), no. 4, 511-518. MR2481688 (2009m: 14084)
34. Li Yi. Some results of the Marino-Vafa formula, Math. Res. Lett., 13(2006), no. 6, 847-864. MR2280780 (2007g: 14071)