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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


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


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


    (17) Li, Yi; Yuan, Yuan; Zhang, Yuguang. On a new geometric flow over Kahler manifolds, to appear in Comm. Analysis and Geometry(CAG#1891, https://www.intlpress.com/site/pub/pages/journals/items/cag/_home/acceptedpapers/index.php)


    (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


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


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


    (13) 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


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


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


    (10) 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


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


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


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


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


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


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


    (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)



    Preprints


    (8) Li, Yi; Yuan, Yuan; Zhang, Yuguang. On a new geometric flow over Kahler manifolds II: local curvatures estimates, preprint, 2020.


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


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


    (5) Li, Yi. Local curvature estimates for the Ricci-harmonic flow, preprint, arXiv: 1810.09760v1 (submitted)


    (4) Li, Yi. Local curvature estimates for Lapalcian G2-flow, preprint, arXiv: 1805.06231 (submitted)


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


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


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



    In preparation



    (1) Li, Yi; Yuan, Yuan; Zhang, Yuguang. On a new geometric flow over Kahler manifolds III: long time behavior, in preparation, 2019.


  • 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 Room2pm-3pm,4/3/2019; School of Mathematics, Jiulonghu Campus
    SpeakerLi 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 Room2pm-3pm,5/10/2019; Rm1511, Yifu Building, Sipailou Campus
    SpeakerMao Jing(Hubei University, China)
    TitleTranslating 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 Room2pm-3pm,6/4/2019; Rm1502, Yifu Building, Sipailou Campus
    SpeakerWang 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. Whats 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 Gurskys work on the Weyl functional 

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

    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



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