教育 EDUCATION：

2008/09-2012/07: Albert-Ludwigs-University Freiburg, PhD in Mathematics

2007/09-2008/08: University of Science and Technology of China, PhD student,

2003/09-2007/07: Sichuan university, Bachlor of Sciences in Mathematics

工作经历WORK EXPERICES：

2015/07-present：Xiamen University, Professor

2018/09-2019/02: Xiamen University Malaysia, Visiting Professor

2015/02-2016/01: McGill University, Postdoc Fellow

2014/09-2015/06：Xiamen University, Associate Professor

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

研究兴趣RESEARCH INTEREST：

Differential Geometry, Geometric Analysis, Nonlinear PDEs, Mathematical Physics,

Topics Including: Geometry of submanifolds, Minimal surfaces, CMC surfaces, Free boundary surfaces, Capillary surfaces, Geometric flows, Geometric inequalities, Geometric PDEs, Riemannian-Finsler Geometry, General Relativity

教学TEACHING

2022/2023 Spring: Riemannian Geometry (graduate)

2022/2023 Fall: Mathematical Analysis III (honors class)

2021/2022 Spring: Mathematical Analysis II (honors class)

2021/2022 Fall: Mathematical Analysis I

2020/2021 Spring: Riemannian Geometry (graduate)

2020/2021 Fall: Mathematical Analysis III

2019/2020 Spring: Differential Geometry (undergraduate honors class)

2019/2020 Fall: Mathematical Analysis III

2018/2019 Fall: Advanced Mathematics I (at XMUMalaysia Campus)

2017/2018 Fall: Differential Geometry (undergraduate honors), Geometric Analysis (graduate)

2016/2017 Fall: Differential Geometry (undergraduate)

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

2014/2015 Fall: Calculus II-1

荣誉与获奖 Awards:

Fujian Province Hundred Talents Plan, 2015

16th Fujian Youth Science and Technology Award, 2021

主持项目GRANTS：

The National Natural Science Foundation of China (Grant No. 12271449): 2023.01-2026.12.

The National Natural Science Foundation of China (Grant No. 11871406): 2019.01-2022.12.

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

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

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

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

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

论文PUBLICATION

53. (with Jinyu Guo) Stable anisotropic capillary hypersurfaces in the half-space, arXiv.2301.03020.

52. (with Xiaohan Jia, Guofang Wang and Xuwen Zhang) Alexandrov’s theorem for anisotropic capillary hypersurfaces in the half-space, Arch. Rational Mech. Anal. 247 (2023), Article number: 25.

51. (with Liangjun Weng and Guofang Wang) Alexandrov-Fenchel inequality for k-convex starshaped capillary hypersurfaces in the half-space, arXiv:2209.13516.

50. (with Xiaohan Jia, Guofang Wang and Xuwen Zhang), Heintze-Karcher inequality and capillary hypersurfaces in a wedge, arXiv:2209.13839.

49. (with Xiaohan Jia and Xuwen Zhang) A Heintze-Karcher type inequality for hypersurfaces with capillary boundary,  J. Geom. Anal. 2023, accepted. arXiv:2203.06931.

48. (with Liangjun Weng and Guofang Wang) Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in the half- space, Math. Ann. 2023, DOI: 10.1007/s00208-023- 02571-4.

47. (with Julian Scheuer) Stability for Serrin’s problem and Alexandroff’s theorem in warped product manifolds, Intern. Math. Res. Not. IMRN 2022, DOI: 10.1093/imrn/rnac294.

46. (with Liangjun Weng) Alexandrov-Fenchel inequality for convex hypersurfaces with capillary boundary in a ball, Trans. Amer. Math. Soc. 375 (2022), no. 12, 8851-8883.

45. (with Jinyu Guo and Guofang Wang) Stable capillary hypersurfaces supported on a horosphere in the hyperbolic space, Adv. Math. 409 (2022), 108641.

44. (with Tao Qiang) Compact hypersurfaces of prescribed mean curvature with free boundary in a ball, Ann. Global Anal. Geom. 61 (2022) no. 3, 679-689.

43. (with Xuwen Zhang) Volume-constraint local energy-minimizing sets in a ball, arXiv:2106.14780.

42. (with Jinyu Guo) A partially overdetermined problem in domains with partial umbilical boundary in space forms,  Adv. Calc. Var. 2022, accepted, arXiv: 2001.10397.

41. (with Changwei Xiong) Escobar's conjecture on a sharp lower bound for the first nonzero Steklov eigenvalue, Peking Math. J. 2023, accepted. arXiv: 1907.07340.

40. (with Guofang Wang) Hsiung-Minkowski's formula for hypersurfaces and their applications, Proceedings of the 8th ICCM, accepted.

39. (with Tao Qiang and Liangjun Weng) A locally constrained mean curvature type flow with free boundary in a hyperbolic ball, Proc. Amer. Math. Soc., 2021, accepted.

38. (with Jiabin Yin) Two overdetermined problems for anisotropic $p$-Laplacian, Math. Engineering, 4 (2022) Issue 2: 1-18.

37. (with Francesco Della Pietra, Nunzia Gavitone) Motion of level sets by inverse anisotropic mean curvature, Comm. Anal. Geom. 2020, accepted, arXiv: 1804.06639.

36. (with Guofang Wang) Guan-Li type mean curvature flow for free boundary hypersurfaces in a ball, Comm. Anal. Geom. 2020, accepted, arXiv: 1910.07253.

35. (with Jiabin Yin) The anisotropic $p$-capacity and the anisotropic Minkowski inequality, Sci. China Math. 65 (2022) 559–582.

34. (with Julian Scheuer, Guofang Wang) Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball,  J. Differential Geom. 120 (2022) no. 2, 345-373.

33. (with Jinyu Guo) Stability for a second type partitioning problem, J. Geom. Anal., 31 (2021), Issue 3, 2890 - 2923.

32. (with Francesco Della Pietra, Nunzia Gavitone) Symmetrization with respect to mixed volumes, Adv. Math. 388 (2021) 107887.

31. (with Jinyu Guo) A partially overdetermined problem in a half ball, Calc. Var. PDE, 58 (2019), Issue 5, Article: 160.

30. (with Guofang Wang) Rigidity of free boundary CMC hypersurfaces in a ball, Surveys in Geometric Analysis, 2018, 138-153.

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, Trans. Amer. Math. Soc. 372 (2019), no. 10, 6771-6803.

27. (with Guofang Wang) Uniqueness of stable capillary hypersurfaces in a ball, Math. Ann., 374 (2019) Issue 3-4, 1845-1882.

26. (with Guohuan Qiu) Classical Neumann Problems for Hessian equations and Alexandrov-Fenchel's inequalities, Intern. Math. Res. Not. IMRN, 2019 (2019) Issue 20, 6285-6303.

25. (with Junfang Li) An integral formula and its applications on sub-static manifolds, J. Differ. Geom., 113 (2019), no.3, 493-518.

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

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,  Intern. 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.

学生培养 Students Supervision

Postdocs:

Jiabing Yin (2019-2021, now Lecturer at Guangxi Normal University)

Xiaohan Jia (2021-)

PhD Students:

Jinyu Guo (2017-2022, now Postdoc at Tsinghua University)

Tao Qiang (2018-2022, now Lecturer at Jiangsu University)

Xuwen Zhang (2019-)

Zheng Lu (2020-)

Xingjian Zhou (2022-)

Master Students:

Zhihui Hou (2016-2019, Primary school teacher)

Tao Qiang (2016-2018, promote to PhD)

Yujin Xi (2017-2020, go to Industry)

Mingxuan Yang (2017-2020, now PhD student at Tsinghua)

Zheng Lu (2018-2020, promote to PhD)

Xingjian Zhou (2020-2022, promote to PhD)

Yangsen Xie (2021-)

Debin Huang (2021-)

Jincong Zheng (2022-)

For more information, see my  CV Xia2023.pdf(last updated: March 2023)