刘磊-华中师范大学数学学院中文站

刘磊

English Version (英文版)

职称教授
办公室六号楼M334
邮箱leiliu2020@ccnu.edu.cn

个人简介

刘磊，男，党员，1988年12月出生于安徽省六安市。2014年博士毕业于中国科学技术大学，主要的研究兴趣包括调和映射、Dirac-调和映射及其热流、半线性椭圆方程和椭圆系统的紧性问题等。论文发表在 Mem. Amer. Math. Soc. 、J. Reine Angew. Math.、Math. Ann.、Adv. Math.、J. Math. Pures Appl.、Ann. Inst. H. Poincare Anal. Non Lineaire、J. Funct. Anal.、Calc. Var. PDE、CAG、Math.Z.等国际期刊。

开设课程

线性代数；微分几何；数学分析；

研究方向

几何分析

教育经历

2009.09-2014.06，中国科学技术大学，博士；
2005.09-2009.06，安徽大学，学士；

工作经历

2020.11-今，华中师范大学数学与统计学学院，教授；
2018.11-2020.11，德国弗莱堡大学（University of Freiburg），博士后；
2015.06-2018.11，德国莱比锡马普数学所（Max Planck Institute for Mathematics in the Sciences, Leipzig），博士后；
2014.06-2015.06，清华大学，博士后；

研究成果

已发表论文：

1. Liu Lei, No neck for Dirac-harmonic maps, Calc. Var. Partial  Differential Equations 52 (2015), no. 1-2, 1-15.

2. Liu Lei and Yin Hao, On the finite time blow-up of biharmonic map flow in dimension four, J. Elliptic Parabol. Equ. 1 (2015), 363-385.

3. Liu Lei and Yin Hao, Neck analysis for biharmonic maps, Math. Z. 283 (2016), no. 3-4, 807-834.

4. Jost Juergen, Liu Lei and Zhu Miaomiao, Blow-up analysis for approximate Dirac-harmonic maps in dimension 2 with applications to the Dirac-harmonic heat flow, Calc. Var. Partial Differential Equations 56 (2017), no. 4, Paper No. 108, 26 pp.

5. Li Yuxiang, Liu Lei and Wang Youde, Blowup behavior of harmonic maps with finite index, Calc. Var. Partial Differential Equations 56 (2017), no. 5, Paper No. 146, 16 pp.

6. Han Xiaoli, Jost Juergen, Liu Lei and Zhao Liang, Bubbling analysis for approximate Lorentzian harmonic maps from Riemann surfaces, Calc. Var. Partial Differential Equations 56 (2017), no. 6, Paper No. 175, 31 pp.

7. Jost Juergen, Liu Lei and Zhu Miaomiao, A global weak solution of the Dirac-harmonic map flow, Ann. Inst. H. Poincare Anal. Non Lineaire 34 (2017), no. 7, 1851-1882.

8. Jost Juergen, Liu Lei and Zhu Miaomiao, Energy identity for a class of approximate Dirac-harmonic maps from surfaces with boundary, Ann. Inst. H. Poincare Anal. Non Lineaire 36 (2019), no. 2, 365-387.

9. Li Jiayu and Liu Lei, Partial regularity of harmonic maps from a Riemannian manifold into a Lorentzian manifold. Pacific J. Math. 299 (2019), no. 1, 33-52.

10. Jost Juergen, Liu Lei and Zhu Miaomiao, The qualitative behavior at the free boundary for approximate harmonic maps from surfaces, Math. Ann. 374 (2019), no. 1-2, 133-177.

11. Jost, Juergen, Liu Lei and Zhu Miaomiao, Asymptotic analysis for Dirac-harmonic maps from degenerating spin surfaces and with bounded index. Calc. Var. Partial Differential Equations 58 (2019), no. 4, Paper No. 142, 33 pp.

12. Han Xiaoli, Jost Juergen, Liu Lei and Zhao Liang, Global existence of the harmonic map heat flow into Lorentzian manifolds, J. Math. Pures Appl. (9) 130 (2019), 130-156.

13. Jost Juergen, Liu Lei and Zhu Miaomiao, Bubbling analysis near the Dirichlet boundary for approximate harmonic maps from surfaces, Comm. Anal. Geom. 27 (2019), no. 3, 639-669.

14. Jost Juergen, Liu Lei and Zhu Miaomiao, Regularity of Dirac-harmonic maps with $\lambda$-curvature term in higher dimensions, Calc. Var. Partial Differential Equations 58 (2019), no. 6, Paper No. 187, 24 pp. 

15. Han Xiaoli, Liu Lei and Zhao Liang, A global weak solution to the Lorentzian harmonic map flow, Sci. China Math. 63 (2020), no. 1, 155-166.

16. Liu Lei and Zhu Miaomiao, Boundary value problems for Dirac-harmonic maps and their heat flows, Vietnam J. Math. 49 (2021), no. 2, 577–596. Special Issue dedicated to Juergen Jost on the occasion of his 65th birthday.

17. Li Jiayu, Liu Lei, Zhu Chaona and Zhu Miaomiao, Energy identity and necklessness for $\alpha$-Dirac-harmonic maps into a sphere, Calc. Var. Partial Differential Equations 60 (2021), no. 4, Paper No. 146.

18. Liu Lei and Wang Guofang, The blow-up analysis of an affine Toda system corresponding to superconformal minimal surfaces in $S^4$,  J. Funct. Anal. 281 (2021), no. 9, Paper No. 109194, 43 pp

19. Jost Juergen, Liu Lei and Zhu Miaomiao, A mixed elliptic-parabolic boundary value problem coupling a harmonic-like map with a nonlinear spinor, J. Reine Angew. Math. (Crelle's Journal)  785 (2022), 81-116.

20. Liu Lei, Song Chong and Zhu Miaomiao, Harmonic maps with free boundary from degenerating bordered Riemann surfaces, J. Geom. Anal. 32 (2022), no. 2, 49.

21. Jost Juergen, Liu Lei and Zhu Miaomiao, Asymptotic analysis and qualitative behavior at the free boundary for Sacks-Uhlenbeck $\alpha$-harmonic maps,  Adv. Math. 396 (2022), Paper No. 108105

22. Jost Juergen, Liu Lei and Zhu Miaomiao, Geometric analysis of the action functional of the nonlinear supersymmetric sigma model,  Calc. Var. Partial Differential Equations 61 (2022), no. 3, Paper No. 112, 26 pp

23. Bi Yuchen, Li Jiayu, Liu Lei and Peng Shuangjie, The C^0-convergence at the Neumann boundary for Liouville equations, Calc. Var. Partial Differential Equations 62 (2023), no. 3, Paper No. 107, 26 pp.

24. Liu Lei, Wang Guofang and Weng Liangjun, The relative isoperimetric inequality for minimal submanifolds in the Euclidean space, J. Funct. Anal. 285 (2023), no. 2, Paper No. 109945, 22 pp

25. Liu Lei and Zhu Miaomiao, Asymptotic analysis for Sacks-Uhlenbeck $\alpha$-harmonic maps from degenerating Riemann surfaces, Memoirs of the American Mathematical Society, 303 (2024), no.1525, ISBN: 978-1-4704-7211-5; 978-1-4704-7994-7

26. Chen Youmin, Liu Lei and Zhu Miaomiao, Bubbling analysis for a nonlinear Dirac equation on surfaces, Acta Math. Scientia. Ser. B (Engl. Ed.), 2024, 44B (6):2073-2082

27. Ai Wanjun, Liu Lei and Zhu Miaomiao, Boundary blow-up analysis for approximate Dirac-harmonic maps into certain Lorentzian manifolds, Sci. China Math., https://doi.org/10.1007/s11425-023-2267-9

待发表文章：

1. Jost Juergen, Liu Lei and Zhu Miaomiao, Geometric analysis of a mixed elliptic-parabolic conformally invariant boundary value problem, MPI MIS Preprint 41/2018.

2. Li Jiayu and Liu Lei, The qualitative behavior at a vortex point for the Chern-Simon-Higgs equation, arXiv:2306.03687

3. Liu Lei and Zhu Miaomiao, Blow-up analysis and energy identities for super-sinh-Gordon type equation, preprint

研究项目

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