中國人民大學(xué)信息學(xué)院基礎(chǔ)數(shù)學(xué)導(dǎo)師介紹：楊云雁

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楊云雁，1971年出生于安徽淮北。

教育背景

1991年9月至1998年6月，在安徽大學(xué)數(shù)學(xué)系學(xué)習(xí)，獲得理學(xué)學(xué)士和理學(xué)碩士學(xué)位。1998年9月至2001年6月，在中科院數(shù)學(xué)所學(xué)習(xí)，獲理學(xué)博士學(xué)位。

工作經(jīng)歷

2001年7月至2003年6月，在北京大學(xué)數(shù)學(xué)科學(xué)學(xué)院從事博士后研究工作。2003年7月至今在中國人民大學(xué)信息學(xué)院工作。

研究興趣

橢圓型偏微分方程，幾何分析

研究課題

1.Moser-Trudinger不等式及預(yù)定Q-曲率問題

2.黎曼流形上偏微分方程解的量子化問題

開設(shè)課程

1.數(shù)學(xué)分析

2.偏微分方程

3.微分幾何

近期發(fā)表的論文選列

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.