陈兵龙 Bing-Long Chen

 

 陈兵龙，1974年生于山西，中共党员。1992-2000年，就读于广州中山大学数学系，获博士学位。2000年于中山大学数学系任讲师，2004年任教授。 2010年获国家杰出青年科学基金， 2014年获教育部长江学者特聘教授，2016年获万人计划领军人才，2022年获中国数学会陈省身数学奖。       

 

 

 

系别：数学系

电话:020-84113005

职称:教授

邮箱:mcscbl@mail.sysu.edu.cn

 

研究方向 ：几何分析

研究成果：

Publication List

 

00. Complete Riemannian manifolds with pointwise pinched curvature, Invent. Math., 140 (2000), 423–452, with Xi-Ping Zhu. 

02. A gap theorem for complete noncompact manifolds with nonnegative curvature, Comm. Anal. Geom. 10(2002),217-239, with Xi-Ping Zhu.

03. Ricci flow on compact Kahler manifolds of positive bisectional curvature, C. R. Acad. Sci. Paris. Ser., I 337(2003), 781–784, with Huai-Dong Cao, Xi-Ping Zhu.

03. On complete noncompact Kahler manifolds with positive bisectional curvature, Math. Ann., 327, 1–23, (2003), with Xi-Ping Zhu.

04. A uniformization theorem of complete noncompact Kahler surfaces with positive bisectional curvature, J. Diff. Geom., 67, 519-570 (2004), with Siu-Hung Tang, Xi-Ping Zhu.

06. Sharp dimension estimates of holomorphic functions and rigidity, Trans. Amer. Math. Soc. 358(2006), no. 4, 1435-1454, with Xiao-Yong Fu, Le Yin, Xi-Ping Zhu.

   Abstract:  Let Mn be a complete noncompact K¨ahler manifold of complex dimension n with nonnegative holomorphic bisectional curvature. Denote by Od(Mn) the space of holomorphic functions of polynomial growth of degree at most d on Mn. In this paper we prove that dimCOd(Mn) ≤ dimCO[d](Cn), for all d > 0, with equality for some positive integer d if and only if Mn is holomorphically isometric to Cn. We also obtain sharp improved dimension estimates when its volume growth is not maximal or its Ricci curvature is
positive somewhere.

06. Ricci Flow with Surgery on Four-manifolds with Positive Isotropic Curvature, J. Diff. Geom., 74 (2006), 177-264, with Xi-Ping Zhu.

06. Uniqueness of the Ricci Flow on Complete Noncompact Manifolds, J. Diff. Geom., 74 (2006), 119-154, with Xi-Ping Zhu.

  Abstract: The Ricci flow is an evolution system on metrics. For a given metric as initial data, its local existence and uniqueness on compact manifolds were first established by Hamilton [9]. Later on, De Turck [5] gave a simplified proof. In the later part of 80’s, Shi
[21] generalized the local existence result to complete noncompact manifolds. However, the uniqueness of the solutions to the Ricci
flow on complete noncompact manifolds is still an open question. In this paper, we give an affirmative answer for the uniqueness
question. More precisely, we prove that the solution of the Ricci flow with bounded curvature on a complete noncompact manifold
is unique.

07. Uniqueness and pseudolocality theorems of mean curvature flow, Comm. Anal. Geom, 15(3),25-80, (2007), with Le Yin.

08. Injectivity radius of Lorentzian manifolds, Comm. Math. Phys. 278 (2008), no. 3, 679-713, with Philippe G. LeFloch.

09. Local foliations and optimal regularity of Einstein spacetimes, J. Geom. Phys. 59 (2009), no. 7, 913-941, with Philippe G. LeFloch.

09. Strong uniqueness of the Ricci flow, J. Diff. Geom. 82 (2009), no. 2, 363-382.

     Abstract: In this paper, we derive some local a priori estimates for the Ricci flow. This gives rise to some strong uniqueness theorems. As a corollary, let g(t) be a smooth complete solution to the Ricci flow on R3, with the canonical Euclidean metric E as initial data, then g(t) is trivial, i.e. g(t) ≡ E.

12. Smoothing positive currents and the existence of Ka ̈hler-Einstein metrics, Sci. China Math. 55 (2012), no. 5, 893-912.

12. Complete classification of compact four-manifolds with positive isotropic curvature, J. Diff. Geom, volume 91 (2012), 41-80, with S.-H. Tang, X.-P. Zhu.

     Abstract: In this paper, we completely classify all compact 4-manifolds with positive isotropic curvature. We show that they are diffeomorphic to S4 or RP4 or quotients of S3 × R by a cocompact fixed point free subgroup of the isometry group of the standard metric of S3 × R, or a connected sum of them.

13. Local pinching estimates in 3-dim Ricci flow, Math. Res. Lett. 20 (2013), no. 5, 845-855, with Xu Guoyi; Zhang Zhuhong.

14. A conformally invariant classification theorem in four dimensions, Comm. Anal. Geom. 22 (2014), no. 5, 811-831, with Xi-Ping Zhu.

14. Self-pairings on supersingular elliptic curves with embedding degree three, Finite Fields Appl. 28 (2014), 79-93, with Zhao Chang-An.

15. Isometric embedding of negatively curved complete surfaces in Lorentz-Minkowski spaces, Pacif Jour. Math., vol. 276, no. 2, (2015), 347-367, with Le Yin.  

    Abstract:  The Hilbert–Efimov theorem states that any complete surface with curvature bounded above by a negative constant cannot be isometrically embedded in R3. We demonstrate that any simply connected smooth complete surface with curvature bounded above by a negative constant admits a smooth isometric embedding into the Lorentz–Minkowski space R2,1.

16. Path-connectedness of the moduli spaces of metrics with positive isotropic curvature on four- manifolds. Math. Ann. 366 (2016), no. 1-2, 819-851, with Xian-Tao Huang. 

    Abstract:  We prove the path connectedness of the moduli spaces of metrics with positive isotropic curvature on certain compact four-dimensional manifolds. 

 17.  Euler characteristic numbers of spacelike manifolds, Asian J. Math. Vol. 21,     No. 3(2017), pp. 591-598. with Kun Zhang.  

   Abstract:  In this note, we prove that if a compact even dimensional manifold Mn with negative sectional curvature is homotopic to some compact space-like manifold Nn, then the signed Euler characteristic number of M is positive.  We also show that the minimal volume conjecture of Gromov is true for all compact even dimensional space-like manifolds. 

 

18. Compact Kähler manifolds homotopic to negatively curved Riemannian manifolds, Math. Ann.,  370(2018): 1477–1489, with Xiaokui Yang. 

     Abstract: In this paper, we show that any compact Kähler manifold homotopic to a compact Riemannian manifold with negative sectional curvature admits a Kähler– Einstein metric of general type. Moreover, we prove that, on a compact symplectic manifold X homotopic to a compact Riemannian manifold with negative sectional curvature, for any almost complex structure J compatible with the symplectic form, there is no non-constant J -holomorphic entire curve f : C → X .

19. On stationary solutions to the vacuum Einstein field equations, Asian J. Math. Vol.23 (2019), No. 4, 609-630.

     Abstract:  We prove that any 4-dimensional geodesically complete spacetime with a timelike
Killing field satisfying the vacuum Einstein field equation Ric(gM) = λgM with nonnegative cosmological constant λ ≥ 0 is flat. When dim ≥ 5, if the spacetime is assumed to be static additionally, we prove that its universal cover splits isometrically as a product of a Ricci flat Riemannian manifold and a real line R.   

19. On stationary solutions to the non-vacuum Einstein field equations, Math. Z. (2019) 293:1227-1246 . 

21. On Euler characteristic and fundamental  groups of compact manifolds, Math. Ann., 381(2021),  1723-1743, with Xiaokui Yang. 

Abstract：Let M be a compact Riemannian manifold, π : M → M be the universal covering and ω be a smooth 2-form on M with π∗ω cohomologous to zero. Suppose the fundamental group π1(M) satisfies certain radial quadratic (resp. linear) isoperimetric inequality, we show that there exists a smooth 1-form η on M of linear (resp. bounded) growth such that π∗ω = dη. As applications, we prove that on a compact Kähler manifold (M, ω) with π∗ω cohomologous to zero, if π1(M) is CAT(0) or automatic (resp. hyperbolic), then M is Kähler non-elliptic (resp. Kähler hyperbolic) and the Euler characteristic (−1)dimR M2 χ(M) ≥ 0 (resp. > 0)

学习经历：

1992.9-1996.7, 广州中山大学数学系本科应用数学专业 获学士学位；

1996.9--2000.7，广州中山大学数学系基础数学专业   获博士学位。

工作经历：

2000－2004  广州中山大学数学系讲师

2004－  今  广州中山大学数学系教授