博士生导师

刘艳楠

教授,博士生导师

通讯地址:北京工商大学数学与统计学院,邮编:100048
电子信箱:liuyn@th.btbu.edu.cn

办公室:阜成路西区综合楼1102

电话:010-68985255

个人简历

20027月毕业于内蒙古大学数理基地班,获学士学位;

20047月毕业于南京理工大学应用数学专业,获硕士学位;

20077月毕业于清华大学应用数学专业,获博士学位;

20077月至20096月,北京大学博士后;

20096月至今,北京工商大学数学系任教;

访问经历:

20096月访问新加坡国立大学;

20107月至9月访问意大利国际理论物理中心。

201212月至201310月, 美国圣母大学,博士后。

研究领域:主要研究几何中的偏微分方程和曲率流,尤其是非线性椭圆方程解的存在性、唯一性和正则性,曲率流的长时间存在性、收敛性和奇点分析

主讲课程:数学分析(全英),线性代数,概率论与数理统计(中、英文)。

承担项目:

1. 凸几何中蒙日-安培型方程的研究,国家自然科学基金面上项目,2021.1-2024.12,主持;

2. 几何中一类退化蒙日安培类型方程的研究,北京市自然科学基金面上项目,2017.1-2019.12,主持;

3. 有关Willmore若干问题的研究,国家自然科学基金青年基金,2013.1-2015.12,主持; 

4. 有关Willmore奇点问题的研究,北京市自然科学基金面上项目,2013.1-2015.12,主持; 

5. 仿射平均曲率流的研究与应用,北京市属高校高层次人才引进与培养:青年拔尖人才资助,2013.1-2015.12,主持; 

6. 一类四阶曲率流奇点发生时间与曲率渐近性质的研究,北京市组织部优秀人才项目,2012.9-2014.12,主持; 

7. 有关Willmore流长时间存在性与收敛性问题的研究,国家自然科学基金天元基金,2011.1-2011.12 主持; 

8. 有关四阶曲率流的研究,中国博士后科学基金,2008.7-2009.6,主持。

发表的主要论文:

[1] Liu Y. N. and Lu J., A flow method for the dual Orlicz-Minkowski problem, Trans. Amer. Math. Soc., 373 (2020): 5833--5853.

[2] Liu, Y. N. and Lu, J., A generalized Gauss curvature flow related to the Orlicz-Minkowski problem. arXiv:2005.02376.

[3] Chen L., Liu, Y. N., Lu, J. and Xiang, N., Existence of smooth even solutions to the dual Orlicz-Minkowski problem. arXiv:2005.02639.

[4] Ju H. J., Li B. Y. and Liu Y. N., Deforming a convex hypersurface by anisotropic curvature flows, to appear in Advanced Nonlinear Studies.

[5] Liu Y. N., Inscribed radius estimates for inverse curvature flow in sphere and hyperbolic space, Nonlinear Analysis, 2017, 155:198-206.

[6] Liu Y. N. and Ju H. J., Non-collapsing for a fully nonlinear inverse curvature flow, Commu. Pure App. Anal., 2017, 16(3): 945-952.

[7] Liu Y. N. and Ju H. J., Evolution of convex surfaces by a fully nonlinear flow, Nonlinear Analysis, T. M. A., 2016, 130: 47-58.

[8] Ju H. J. and Liu Y. N., Dirichlet problem for anisotropic prescribed mean curvature equation on unbounded domains, J. Math. Anal. Appl., 2016(439): 709-724.

[9] Han Q. and Liu Y. N., Degenerate hyperbolic equations with low degree degeneracy, Pro. Amer. Mathematical Society, 2015, 143(2): 567-580

[10] Liu Y. N., Inverse mean curvature flow with forced term, J. Math. Anal. Appl. 2014(410): 918-931.

[11] Liu Y. N. and Cao L. F., Lifespan theorem and Gap lemma for the globally constrained Willmore flow, Comm. Pure Appl. Anal.,2014, 13(2):715-728.

[12] Liu Y. N., Gradient flow of the Helfrich functional, Chin. Ann. Math., 2012, 33(6): 931-940.

[13] Liu Y. N., Evolution of hypersurfaces by powers of mean curvature, Front. Math. China. 2012, 7(4): 717-724.

[14] Jian H Y and Liu Y. N., Ginzburg-Landau vortex and mean curvature flow with external force field. Acta. Math. Sin., Engl. Ser. 2006, 22(6): 1831-1842.

[15]Liu Y. N. and  Jian H. Y., Evolution of hypersurfaces by mean curvature minus external force field. Science in China (Ser A). 2007, 50(2): 231-239.

[16] Jian H Y and Liu Y. N., Long-time existence of mean curvature flow with external force fields. Pacific J. Math. 2008, 234(2), 311-324.

[17] Liu Y. N. and  Jian H. Y., Evolution of spacelike hypersurfaces by mean curvature minus external force field in Minkowski space.  Advanced Nonlinear Studies, 2009, 9513-522.

[18] Liu Y. N. and  Jian H. Y., A curve flow evolved by a fourth order parabolic equation. Science in China, Ser A, 2009, 52(9): 21772184.

[19] Liu Y. N., Evolution of noncompact hypersurfaces  by mean curvature minus a kind of external force field,   Front. Math. China, 2010, 5(2): 311-317.

[20] Jian H. Y., Ju H. J. and Liu Y. N., and Sun W., Symmetry of  translating solutions to mean curvature flowsActa Mathematica Scientia2010,30B(6):2006–2016.