数学学院

Li，Yi

Professor

Shing-Tung Yau Center of Southeast University

Applied Mathematics Department

Tel:

Email:

yilicms@seu.edu.cn, yilicms@gmail.com, yilicms@163.com

Address:

1511

Post:

210096

I am interested in differential geometry, complex geometry, geometric analysis, geometric flow, nonlinear geometric type PDEs, and general relativity and their applications.

*Appointment* (1) 2019/3-now: Full Professor, School of Mathematics, Southeast University and S.-T. Yau Center of Southeast University, (2) 2018/12-2019/2: Visiting Professor, S.-T. Yau Center of Southest University, (3) 2016/12-2018/11: Assistant-Chercheur, Department of mathematics, Universite du Luxembourg (4) 2014/3-2014/6: Visiting Professor, Shanghai Center for Mathematical Sciences (5) 2013/6-2016/11, Special Researcher, department of mathematics, Shanghai Jiao Tong University (6) 2012/6-2013/5: Lecturer, Department of Mathematics, Johns Hopkins University

*Education* Ph.D. Mathematics, Harvard University, U.S.A., 2007-2012. M.S. Mathematics, Zhejiang University, China, 2004-2007. B.S. Mathematics, Ningbo University, China, 2000-2004.
Publications and Preprints

(34) Li, Yi; Zhang, Qianwei. Existence of solutions to a class of Kazdan-Warner equations on finite graphs, preprint, arXiv: 2308.10002, 2023 (submitted)

(33) Li, Yi. Curvature pinching estimate under the Laplacian G_2 flow, preprint, arXiv: 2307.14289, 2023 (submitted)

(32) Li, Yi. Curvature estimates on a parabolic flow of Fei-Guo-Phong, preprint, arXiv: 2210.16842, 2022 (submitted)

(31) Li, Yi. A new notion on weighted Riemann curvature, Rendiconti del Circolo Matematico di Palermo Series 2, 2023.

(30) 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).

(29) Li, Yi; Li, Chuanhuan. List's flow with bounded integral curvature on noncompact complete Riemannian manifolds, preprint, 2022

(28) 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)

(27) Li, Yi. Local curvature estimates for the Ricci-harmonic flow, Nonlinear Analysis, 222(2022), No. 112961, 53pp.

(26) Li, Yi; Yuan, Yuan. Local curvature estimates along the k-LYZ flow, J. Geom. Phys., 164(2021), 104162, 21pp.

(25) Li, Yi. Local curvature estimates for the Laplacian flow,  Cal. Var. PDE., 60(2021), no. 1, Paper No. 28, 37pp.

(24) Li, Yi; Yuan, Yuan; Zhang, Yuguang. On a new geometric flow over Kahler manifolds, Comm. Analysis and Geometry, 28(2020), no. 6, 1251-1288.

(23) Zhu, Xiaorui; Li, Yi. Harnack estimates for a heat-type equation under the geometric flow, Potential Analysis, 52(2020), 469-496. MR4067300

(22) Li, Yi. Generalized Ricci flow II: existence for noncompact complete manifolds, Differential Geometry and its Applications, 66(2019), 106-154. MR3913713

(21) Li, Yi. Scalar curvature along the Ricci flow, preprint, 2019 (submitted).

(20) Li, Xiangdong; Li, Songzi; Li, Yi. Uniqueness and local curvature estimates for a class of generalized Ricci flow, preprint, 2019.

(19) Li, Yi. Long time existence and bounded scalar curvature in the Ricci-harmonic flow, J. Differential Equations, 265(2018), no. 1, 69-97. MR3782539

(18) Li, Yi; Zhu, Xiaorui. Harnack estimates for a nonlinear equation under Ricci flow, Differential Geometry and its Applications, 56(2018), 67-80. MR3759353

(17) Wu, Guoqiang; Li, Yi. Heat kernel estimates along the Ricci-harmonic flow, preprint, 2017 (submitted)

(16) Li, Yi. Long time existence of Ricci-harmonic flow, Front. Math. China, 11(2016), no. 5, 1313-1334. MR3547931

(15) 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

(14) Li, Yi. Li-Yau-Hamilton estimates and Bakry-Emery Ricci curvature, Nonlinear Anal., 113(2015), 1-32. MR3281843

(13) Li, Yi; Liu, Kefeng. A geometric heat flow for vector fields, Sci. China Math., 58(2015), no. 4, 673-688.MR3319305

(12) 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

(11) Li, Yi. A priori estimates for Donaldson's equation over compact Hermitian manifolds, Cal. Var. PDE., 50(2014), no. 3-4, 867-882. MR3216837

(10) Li, Yi. On an extension of the H^k-mean curvature flow for closed convex hypersurfaces, Geom. edicata,172(2014), 147-154. MR3253775

(9) Li, Yi. Eigenvalues and entropies under the harmonic-Ricci flow, Pacific J. Math.,267
(2014), no. 1, 141-184. MR3163480

(8) Li, Yi. Mabuchi and Aubin-Yau functionals over complex surfaces, J. Math. Anal. Appl., 416(2014), no. 1, 81-98. MR3182749

(7) Li Yi. On an extension of the H^k-mean  curvature flow, Sci. China Math., 55(2012), no. 1, 99-118. MR2873806

(6) Li, Yi. Generalized Ricci flow I: higher derivatives estimates for compact manifolds, Analysis & PDE, 5(2012), no. 4, 747-775. MR3006641

(5) Li, Yi. Mabuchi and Aubin-Yau functionals over complex manifolds, arXiv: 1004.0553, preprint.

(4) Li, Yi. Mabuchi and Aubin-Yau functionals over complex three-folds, arXiv: 1003.5307, preprint.

(3) Li Yi. Harnack inequality for the negative power Gaussian curvature flow, Proc. Amer. Math. Soc., 139(2011), no. 10, 3707-3717. MR2813400 (2012g: 53137)

(2) 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)

(1) Li Yi. Some results of the Marino-Vafa formula, Math. Res. Lett., 13(2006), no. 6, 847-864. MR2280780 (2007g: 14071)

In preparation

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

Shing-Tung Yau Center of Southeast University

https://yauc.seu.edu.cn/yaucen/main.htm

Honors

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

Grants

1. Participant, NSFC No. 11826031, 2019/1-2019/12

2.Principal Applicant, NSFC No. 11401374, 2015/1 - 2017/12,

3.Principal Applicant, Shanghai Sailing (YangFan) Project No. 14YF1401400, 2014/7 - 2017/6,

4.Participant, Fonds National de la Recherche Luxembourg (FNR) unde the OPEN scheme (project GEOMREV O14/7628746), 2015 - 2018,

Teaching

1.2020 Spring: Differential Manifolds,

2.2020 Spring: Mathematical Analysis II

3.2020 Fall: Topology

4.2020 Fall: Mathematical Analysis I.

Undergraduate Seminar

1.2019 Fall: Topology

2.2019 Fall: Honor Calclus

Seminar and Conference

Time and Room	2pm-3pm,4/3/2019; School of Mathematics, Jiulonghu Campus
Speaker	Li Jiongyue (Tsinghua University, China)
Title	Asymptotic properties of the spinor field and the application to nonlinear Dirac model
Abastract	In this talk, we will first discuss the asymptotic behavior of the linear solutions of massless Dirac equations in R1+3. It is proved that the solutions decay in a sharp rate and enjoy the so-called peeling properties. Based on this decay mechanism of the linear solutions and spinor null condition we raised,we also discuss the small data global existence result for a class of nonlinear Dirac models.

Time and Room	2pm-3pm,5/10/2019; Rm1511, Yifu Building, Sipailou Campus
Speaker	Mao Jing(Hubei University, China)
Title	Translating surfaces of the non-parametric mean curvature flow in Lorentz manifold M^2*R
Abstract	For the Lorentz manifold M^2*R, with M^2 a 2-dimensional complete surface with nonnegative Gaussian curvature, we investigate its space-like graphs over compact strictly convex domains in M^2, which are evolving by the non-parametric mean curvature flow with prescribed contact angle boundary condition, and show thatsolutions converge to ones moving only by translation. This talk is based on a joint-work with L. Chen, D.-D. Hu and N. Xiang.

Time and Room	2pm-3pm,6/4/2019; Rm1502, Yifu Building, Sipailou Campus
Speaker	Wang Lihan(University of Connecticut, USA)
Title	Symplectic Laplacians, boundary conditions and cohomology
Abstract	Symplectic Laplacians are introduced by Tseng and Yau in 2012, which are related to a system of supersymmetric equations from physics. These Laplacians behave different from usual ones in Rimannian case and Complex case. They contain both 2nd and 4th order operators. In this talk, we will discuss these operators and their relations with cohomologies on compact symplectic manifolds with boundary. For this purpose, we will introduce new boundary conditions for differential forms on symplectic manifolds. Their properties and importance will be discussed.

4/10/2019, Geometric Analysis Seminar, School of Mathematics, Jiulonghu Campus

时间

报告人

题目

9:00-9:45

徐国义(清华大学）

Xu Guoyi (Tsinghua University)

The analysis and geometry of isometric embedding

In 1950’s, Nash-Kuiper built up the C¹ isometric embedding for any

surface into R³, this can be viewed as analysis side of isometric embedding.

On the other hand, there is obstruction for the existence of C² isometric

embedding of surface into R³ known since Hilbert, which reflects the geometry

flavor of isometric embedding. What’s happening from C² to C² (from analysis

to geometry)? The talk will be accessible to general audience with basic

knowledge of analysis and geometry.

9:50-10:35

王作勤（中国科学技术大学）

Wang Zuoqin (USTC)

On Weyl Asymptotic

Weyl law, first discovered by H. Weyl in 1911 for the Dirichlet-Laplace

eigenvalues of bounded regions and then extended/strengthened by many

mathematicians to various general settings, relates the asymptotic

behavior of eigenvalues of certain operators with the background geometric/

analytic/dynamic behavior. In this talk I will briefly describe

these connections and discuss some recent work.

10:45-11:30

华波波（复旦大学）

Hua Bobo (Fudan University)

图上的分析和应用

我们研究图和离散Laplace算子。用离散分析的技巧，研究图和Laplace算子的

特征值问题、Schroendinger算子等。

11:35-12:20

来米加（上海交通大学）

Lai Mijia (Shanghai Jiaotong University)

The renormalized volume on 4-dimensional CCE manifolds

The renormalized volume is a very important global invariant for

conformally compact Einstein (CCE) manifolds. In dimension 4, it is the

integral of sigma_2 of the Schouten tensor, which appears in the

Gauss-Bonnet-Chern formula. Based on Gursky’s work on the Weyl functional

and the de Rham cohomology on closed 4-manifolds and Chang-Gursky-Yang’s

conformal 4-sphere theorem, one can deduce interesting topological

consequences for 4-dim CCE manifolds under assumptions on the renormalized

volume. I will survey results in this direction and discuss some recent thoughts.

2019 Young Geometric Analysts Conference, Southeast University

2019年东南大学青年几何分析会议.pdf

Hobby

1. Basketball and Parkour

2. Chinese History after 1840