厦门大学数学科学学院数学与应用数学系导师介绍：夏超

Chao Xia (夏 超)

Address:

School of Mathematical Sciences, Xiamen University,

Siming South Road 422, 361005, P.R. China

Tel.: +86-592-2580-623

Email: chaoxia@xmu.edu.cn

Here is myCV (updated May 2018).

From Fall 2017, I am a co-organizer of the weekly Gometric Analysis seminar at XMU.

Education：

2008/09-2012/07：Albert-Ludwigs-Universität Freiburg, Mathematics, Ph.D. Degree. 

2007/09-2008/08：University of Science and Technology of China, Mathematics, Ph.D. student.

2003/09-2007/07：Sichuan University, Mathematics, Bachelor of Science.

 Employment：

2015/08-Now: Professor, School of Mathematical Sciences, Xiamen University.

2015.02-2016.01: Research Fellow, Department of Mathematics and Statistics, McGill University. 

2014/09-2015/07：Associate Professor, School of Mathematical Sciences, Xiamen University. 

2012/08-2014/08：Postdoc Fellow, Max-Planck institute for Mathematics in the Sciences.

Honors:

Thousand Youth Talents Plan, 2015.

Fujian Province Hundred Talents Plan, 2015.

Funding:

1. Fundamental Research Funds for the Central Universities (Grant No. 20720150012):   2015.01-2017.12.

2.The National Natural Science Foundation of China (Grant No. 11501480): 2016.01-2018.12.

3.The Scientific Research Foundation for the Returned Overseas Chinese Scholars: 2015.05-2018.04.

4. The Natural Science Foundation of Fujian Province of China (Grant No. 2017J06003): 2017.04-2020.03.

5. Fundamental Research Funds for the Central Universities (Grant No. 20720180009):   2018.01-2020.12.

Research interests：

 Geometric analysis and PDEs, including Riemann-Finsler Geometry, Geometry of Submanifolds, Conformal Geometry and related PDE problems.

Publications and Preprints：

31. (with Jinyu Guo) A partially overdetermined problem in a half ball, arXiv: 1807.01507.

30. (with Francesco Della Pietra, Nunzia Gavitone) Motion of level sets by inverse anisotropic mean curvature, arXiv: 1804.06639.

29. (with Pengfei Guan) $L^p$ Christoffel-Minkowski problem: the case $1<p<k+1$, Calc. Var. PDE, 57 (2018), Issue 2, Article: 69.

28. (with Julian Scheuer)  Locally constraint inverse curvature flows, arXiv:1708.06125.

27. (with Guofang Wang) Uniqueness of stable capillary hypersurfaces in a ball, arXiv:1708.06861.

26. (with Guohuan Qiu) Classical Neumann Problems for Hessian equations and Alexandrov-Fenchel's inequalities, Intern. Math. Res. Not. IMRN, 2018, online first.

25. (with Junfang Li) An integral formula and its applications on sub-static manifolds, J. Differ. Geom., 2017, accepted. arXiv: 1603.02201.

24. (with Bobo Hua，Martin Kell) harmonic functions on metric measure spaces, arXiv:1308.3607.

23. Inverse anisotropic mean curvature flow and a Minkowski type inequality, Adv. Math., 315 (2017), 102-129. 

22. (with Xiangwen Zhang) ABP estimate and geometric inequalities, Comm. Anal. Geom., 25 (2017), 685-708.

21. (with Bobo Hua, Shiping Liu) Liouville theorems for f-harmonic maps into Hadamard spaces,  Pac. J. Math. 290 (2017), no.2, 381-402.

20. (with Junfang Li) An integral formula for affine connections, J. Geom. Anal. 27 (2017), no.3,  2539-2556.

19. Inverse anisotropic curvature flow from convex hypersurfaces, J. Geom. Anal. 27 (2017), no.3, 2131-2154.

18. (with Guohuan Qiu) Overdetermined boundary value problems in S^n, J. Math. Study, 50 (2017), 165-173.

17. (with Yuxin Ge, Guofang Wang, Jie Wu) Gauss-Bonnet-Chern mass and Alexandrov-Fenchel inequality, Frontiers of Mathematics in China, 11 (2016), Issue 5, 1207-1237.

16. A Minkowski type inequality in space forms, Calc. Var. PDE, 55 (2016), Issue 4, Article:96.

15. (with Guohuan Qiu) A generalization of Reilly's formula and its applications to a new Heintze-Karcher type inequality,  Intern. Math. Res. Not. IMRN, 2015 (2015) Issue 17, 7608-7619.

14. (with Jie Wu) Hypersurfaces with constant curvature quotients in warped product manifolds.  Pac. J. Math. 274 (2015), No. 2, 355-371.

13. (with Yuxin Ge, Guofang Wang, Jie Wu) A Penrose inequality for graphs over Kottler space.  Calc. Var. PDE, 52 (2015), Issue 3-4, 755-782.

12. Local gradient estimate for harmonic functions on Finsler manifolds, Calc. Var. PDE 51 (2014), Issue 3-4, 849-865.
11. (with Jie Wu) On rigidity of hypersurfaces with constant curvature functions in warped product manifolds,  Ann. Global Anal. Geom. 46(2014), 1-22.

10. (with Bobo Hua) A note on local gradient estimate on Alexandrov spaces, Tohoku Math. J. (2) 66 (2014), 259-267.

9. (with Guofang Wang) Isoperimetric type problems and Alexandrov-Fenchel type inequalities in the hyperbolic space, Adv. Math. 259 (2014), 532-556. 

8. On an anisotropic Minkowski problem, Indiana Univ. Math. J.  62 (2013),  1399-1430. 

7. (with Guofang Wang)  A sharp lower bound for the first eigenvalue in Finsler manifolds,  Ann. IHP(C) Non. Anal., 30 (2013) Issue 6, 983-996.

6. (with Yuxin Ge, Guofang Wang) On problems related to an inequality of De  Lellis and Topping,  Internat. Math. Res. Not. IMRN, 2013 (2013) Issue 20, 4798-4818.

5. (with Yong Luo) Hölder regularity for equations of prescribed anisotropic mean curvature type,  Manuscripta Math., 141 (2013), 589--600.

4. (with Guofang Wang) An optimal anisotropic Poincare inequality for convex domains, Pac. J. Math., 258 (2012) 305--326. 

3. (with Guofang Wang) Blow-up analysis of a Finsler-Liouville equation in two dimensions, J. Differ. Eq., 252 (2012), 1668-1700. 

2. (with Guofang Wang) A Brunn-Minkowski inequality for a Finsler-Laplacian,  Analysis (Munich), 31(2011),103-115.

1. (with Guofang Wang) A characterization of the Wulff shape by an overdetermined anisotropic PDE,  Arch. Rational Mech. Anal., 99 (2011), 99-115.  

Teaching： 

2014/2015 Fall: Calculus II-1.

2015/2016 Spring: Calculus I-2, Differential Geometry (graduate course).

2016/2017 Fall: Diffenretial Geometry (undergraduate course).

2017/2018 Fall: Diffenretial Geometry (undergraduate course), Geometric Analysis  (graduate course).