中国人民大学信息学院基础数学导师介绍：杨云雁

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杨云雁，1971年出生于安徽淮北。

教育背景

1991年9月至1998年6月，在安徽大学数学系学习，获得理学学士和理学硕士学位。1998年9月至2001年6月，在中科院数学所学习，获理学博士学位。

工作经历

2001年7月至2003年6月，在北京大学数学科学学院从事博士后研究工作。2003年7月至今在中国人民大学信息学院工作。

研究兴趣

椭圆型偏微分方程，几何分析

研究课题

1.Moser-Trudinger不等式及预定Q-曲率问题

2.黎曼流形上偏微分方程解的量子化问题

开设课程

1.数学分析

2.偏微分方程

3.微分几何

近期发表的论文选列

1. Yang, Y. (2012): Existence of positive solutions to quasi-linear elliptic equations with exponential growth in the whole Euclidean space, J. Funct. Anal. 262: 1679-1704, Feb, 15.

2. Yang, Y. (2012): Adams type inequalities and related elliptic partial differential equation in dimension four. J. Diff. Equations. 252:2266-2295.

3. Li, J. and Yang, Y. (2012): Nonexistence of quasi-harmonic spheres with large energy. Manuscripta Mathematica 138, 161-169. 

4. Yang, Y. (2011): Smoothing metrics on closed Riemannian manifolds through the Ricci flow. Ann. Global Anal. Geom. 40, 411-425.

5. Adimurthi, A. and Yang, Y. (2011): Multibubble analysis on N-Laplace equation in R^N. Cal. Var. 40, 1-14.

6. Do O, J. M. and Yang, Y. (2010): A quasi-linear elliptic equation with critical growth on compact Riemannian manifold without boundary. Ann. Global Anal. Geom. 38, 317-334.

7. Adimurthi, A. and Yang, Y. (2010): An interpolation of Hardy inequality and Trudinger-Moser inequality in R^N and its applications. International Mathematics Research Notices 13, 2394-2426.

8. Yang, Y. (2010): Gradient estimate for an elliptic equation with sigular nonlinearity. Acta Math. Sinica 26, 1177-1182.

9. Yang, Y. and Zhao, L. (2010): A class of Adams-Fontana type inequalities and related functionals on manifolds. Nonlinear Differential Equations and Applications 17, 119-135.

10. Liu, Q. and Yang, Y. (2010): Rigidity of the harmonic map heat flow from sphere to compact Kahler manifolds. Arkiv for Matematik 48, 121-130

11. Lu, G. and Yang, Y. (2009): Adams’ inequalities for bi-Laplacian and extremal functions in dimension four. Advances in Mathematics 220, 1135-1170.

12. Yang, Y. (2008): Gradient estimates for a nonlinear parabolic equation on Riemannian manifolds. Proc. Amer. Math. Soc. 136, 4095-4102.

13. Yang, Y. (2007): A sharp form of the Moser-Trudinger inequality on a compact Riemannian surface. Trans. Amer. Math. Soc. 359, 5761-5776.