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张树城


个人简介:

张树城, 重庆理工大学教授〪1959年2月27日出生于中国台湾〪1985年大学本科毕业于台湾师范大学,1990年在高志湧教授的指导下获得美国莱斯大学博士学位〪


研究领域:

微分几何,柯西黎曼几何,以及凯勒流形与佐佐木流形上的几何分析


工作经历:

台湾师范大学 数学系 助教, 1981-1982, 1984-1985

台湾清华大学 数学系 副教授, 1990-2000

台湾清华大学 数学系 教授, 2000-2008

台湾清华大学 数学系 主任, 2004-2007

台湾大学 数学系 教授, 2008至今

台湾大学 数学科学中心 研究员, 2008-2017

世界华人数学家联盟年会 执行主任, 2017-2019


访问经历:

哈佛大学 访问学者, 1993/9-1993/12

斯坦福大学 访问学者, 1994/1-1994/6

哈佛大学 访问学者, 1999/5-1999/7

加利福尼亚大学聖地牙哥分校 访问学者, 2002/8-2003/1

清华大学 访问学者, 2017/9-2018/8

美国乔治城大学 访问学者, 2021/10-2022/1


荣誉:

2015台湾数学会学术奖

2017华人数学家年会最佳论文奖


承担的基金项目(中国台湾):

1. 柯西黎曼流形上的几何分析(NSF 099-2115-M-002-007-MY3), 2010/8-2013/7

2. 柯西黎曼流形中的几何化问题(NSF 102-2115-M-002-007-MY3), 2013/8-2016/7

3. 柯西黎曼流形上的几何流(NSF 105-2115-M-002 -007 -MY2), 2016/8-2018/7

4. 柯西黎曼流形中的单值化猜想(MOST 107-2115-M-002-008), 2018/8-2019/7

5. 佐佐木流形上的单值化猜想(MOST 108-2115-M-002 -005-MY2), 2019/8-2021/7

6. 佐佐木-瑞奇流(MOST 110-2115-M-002 -007 -MY3), 2021/8-2024/7


博士生培养:

吴进通, 1997-2002 (现职: 台湾屏东大学数学系教授)

张庭辉, 2006-2010 (现职: 台湾清华大学数学系助理教授)

郭庭榕, 2007-2011 (现职: 台湾师范大学数学系副教授)

赖馨华, 2008-2013 (现职: 台湾中央大学数学系博士后)

樊彦彣, 2009-2014 (现职: 台积电研发工程师)

林乾, 2013-2018 (现职: 重庆理工大学数学科学研究中心特聘副教授)


论文(2000年至今):

1. (with Y.-B. Han, N. Li and C. Lin), Existence of nonconstant CR-holomorphic functions of polynomial growth in Sasakian Manifolds, arXiv:1909.06513. Submitted.

2. (with D.-C. Chang, T.-J. Kuo and C. Lin), Vanishing Theorem of Kohn-Rossi Cohomology Class and Rigidity of Sasakian Space Form, to appear in Pure and Applied Mathematics Quarterly.

3. (with Yingbo Han and Chien Lin), On the sharp dimension estimate of CR holomorphic functions in Sasakian Manifolds, Int. Math. Res. Not. IMRN 2021, no. 17, 12888-12924. 53C25 (32V20); arXiv:1801.07428.

4. (with Huai-Dong Cao and Chih-Wei Chen), C0-positivity and a classification of closed three-dimensional CR torsion solitons, Mathematische Zeitschrift, 296 (2020), no. 3-4, 10651080.

5. (with Y.-X. Dong and Y.-B. Han), On the p-pseudoharmonic map heat flow, International Journal of Mathematics, Vol. 31, No. 13 (2020) 2050104 (27 pages)

6. (with Der-Chen Chang and Chien Lin), On Li-Yau gradient estimate for sum of squares of vector fields up to higher step, Communications in Analysis and Geometry, Volume 28(2020), Number 3, 565-606

7. (with Yingbo Han and Chien Lin), On the three-circle theorem and its applications in Sasakian manifolds, Calc. Var. Partial Differential Equations 58 (2019), no. 3, Art. 101, 23pp.

8. (with Der-Chen Chang, Yingbo Han and Jingzhi Tie), A CR Analogue of Yau’s Conjecture On Pseudoharmonic Functions of Polynomial Growth, CJM, Volume 71 (2019), Issue 6, pp. 1367-1394.

9. (with T.-J. Kuo, C. Lin and J. Tie), CR Sub-Laplacian Comparison and Liouville-type Theorem in a Complete Noncompact Sasakian Manifold, J. Geom. Anal. 29 (2019), no. 2, 1676-1705.

10. (with Huai-Dong Cao and Chih-Wei Chen), On three-dimensional CR Yamabe solitons, J. Geom. Anal. (2018) 28:335-359.

11. (with Der-Chen Chang, Yingbo Han and Chien Lin), On the CR Poincaré-Lelong equation, Yamabe steady solitons and structures of complete noncompact Sasakian manifolds, Acta Mathematica Sinica, English Series, Vol. 34, No. 8, 1313-1344 (2018), a special issue in several complex variables in memory of Prof. Qikeng Lu.

12. (with C.-W. Chen and C.-T. Wu), On the CR Analogue of Reilly Formula and Yau Eigenvalue Conjecture, Asian J. Math., Vol. 22, No. 5 (2018), 919-940.

13. (with Der-Chen Chang, Ting-Jung Kuo and Hsin-Hua Lai), CR Li-Yau gradient estimate for Witten Laplacian via Bakry-Emery pseudohermitian Ricci curvature, Asian J. Math, Volume 22, No. 2, 223 –256 (2018), Special issue in honor of Ngaiming Mok.

14. (with J.-T. Chen and Walter Wei), Liouville properties for p-harmonic maps with finite q-energy, Trans. Amer. Math. Soc. 368 (2016), no. 2, 787-825.

15. (with Y.-W. Fan), An Optimal Gap Theorem in a Complete Strictly Pseudoconvex CR (2n + 1)-manifold, J Geom. Anal. 26 (2016), 2425-2449.

16. (with T.-H. Chang), Finite-Time Blow up and Global Existence for the Heat Flow of Pseudoharmonic Maps, Indiana Univ. Math. J. 64 (2015), no. 2, 441-470.

17. (with J.-T. Chen and T.-J. Kuo), Complete Pseudohermitian Manifolds with Positive Spectrum, J. Geom. Anal. 25 (2015), no. 1, 92-107.

18. (with T.-H. Chang and Y.-W. Fan), Linear trace Li-Yau-Hamilton inequality for the CR Lichnerowicz-Laplacian heat equation, J. Geom. Anal. 25 (2015), no. 2, 783-819.

19. (with D.-C. Chang and J.-Z. Tie), Calabi-Yau Theorem and Hodge-Laplacian Heat Equation in a Closed Strictly Pseudoconvex CR Manifold, J. Differential Geometry, 97(2014), 395-425. Erratum, 102(2016), 351.

20. (with T.-H. Chang), On CR Volume Growth Estimate in a Complete Pseudohermitian 3-manifold, International J. of Mathematics, Vol. 25, No. 4 (2014) 1450035 (22 pages).

21. (with Y.-W. Fan, J. Tie and C.-T. Wu), Matrix Li-Yau-Hamilton Inequality for the CR Heat Equation in Pseudohermitian (2n+1)-manifolds, Math. Ann. 360 (2014), 267-306.

22. (with T.-H. Chang), On the existence of pseudoharmonic maps from pseudohermitian manifolds into Riemannian manifolds with nonpositive sectional curvature, The Asian Journal of Mathematics, Vol. 17 (2013), 1-16.

23. (with C.-T. Wu), The Diameter Estimate and Its Application to CR Obata’s Theorem on Closed Pseudohermitian (2n+1)-Manifolds, Trans. Amer. Math. Soc. 364 (2012), 3349-3363.

24. (with T.-J. Kuo and S.-H. Lai), Li-Yau Gradient Estimate and Entropy Formulae for the CR heat equation in a Closed Pseudohermitian 3-manifold, J. Differential Geom. 89(2011), 185-216.

25. (with Takanari Saotome), The Q-curvature ‡ow in a closed CR 3-manifold, Proceedings of the 15th International Workshop on Differential Geometry and the 4th KNUGRG-OCAM Differential Geometry Workshop [Volume 15], 57-69, Natl. Inst. Math. Sci. (NIMS), 2011

26. (with H.-L. Chiu and C.-T. Wu) The Li-Yau-Hamilton Inequality for Yamabe Flow on a Closed CR 3-Manifold, Transactions of AMS, Vol 362 (2010), 1681-1698.

27. (with C.-T. Wu), The Entropy Formulas for the CR Heat Equation and its Applications on Pseudohermitian (2n+1)-Manifolds, Pacific Journal of Mathematics. 246 (2010), 1-29.

28. (with Jingzhi Tie and C.-T. Wu) Subgradient Estimate and Liouville-type Theorems for the CR Heat Equation on Heisenberg groups H^n, Asian J. Math., Vol. 14, No. 1 (2010), 041-072.

29. (with H.-L. Chiu) Nonnegativity of CR Paneitz operator and its Application to the CR Obata’s Theorem in a Pseudohermitian (2n + 1)-Manifold, Journal of Geometric Analysis, Vol. 19 (2009), 261-287.

30. (with H.-L. Chiu) On the CR Analogue of Obata’s Theorem in a Pseudohermitian 3-Manifold, Math. Ann. Vol. 345, No. 1 (2009), 33-51.

31. (with D.-C. Chang and Jingzhu Tie) Laguerre Calculus and Paneitz Operator on Heisenberg groups H^n, Science in China Series A: Mathematics, 52 (2009), 2549-2569.

32. (with Jianguo Cao) The Modified Calabi-Yau Problems for CR-manifolds and Applications, Nankai Tracts in Mathematics - Vol. 12 (2008), 3-17.

33. (with J.-H. Cheng and H.-L. Chiu) A Fourth Order Curvature Flow on a CR 3-manifold, Indiana Univ. Math. J., Vol. 56, No. 4 (2007), 1793-1826.

34. (with Jianguo Cao) Pseudo-Einstein and Q-Flat Metrics with Eigenvalue Estimates on CR-Hypersurfaces, Indiana Univ. Math. J., Vol. 56, No. 6 (2007), 2840-2857.

35. (with Peng Lu) Evolution of Yamabe Constants under Ricci flow, Annals of Global Analysis and Geometry 31 (2007), 147-153.

36. (with C.-T. Wu) The Fourth-Order Q-Curvature Flow on Closed 3-Manifolds, Nagoya Math. J., Vol. 185 (2007), 1-15.

37. (with H.-L. Chiu) On the Estimate of First Eigenvalue of a Sublaplacian on a Pseudo-Hermitian 3-Manifold, Pacific Journal of Mathematics Vol. 232, No. 2 (2007), 269-282.

38. (with C.-T. Wu), The Bondi-Mass Type Estimate on a Closed CR 3-Manifold with Nonnegative Paneitz Operator, Proceedings of ICCM 2007, Vol. II (2007), 3-28.

39. Three-Manifolds with Small L2-Norm of Traceless-Ricci Curvature Pinching, Annals of Global Analysis and Geometry, Vol 30 (2006), 37-63.

40. The 2-Dimensional Calabi Flow, Nagoya Math. J. Vol. 181 (2006), 63-73.

41. Recent Developments on the Calabi Flow, Contemporary Mathematics, Vol 367, 17-42, AMS, 2005.

42. (with C.-T. Wu) On the Existence of Extremal metrics on Complete Noncompact 3-Manifolds, Indiana Univ. Math. J. 53 (2004), 243-268.

43. (with C.-T. Wu) Extremal metrics for quadratic functional of scalar curvature on closed 3-Manifolds, Annals of Global Analysis and Geometry Vol. 25, No. 1 (2004), 11-25.

44. (with S.-K. Hong, C.-T. Wu) The Harnack Estimate for the Modified Ricci flow on Complete R2; Rocky Mountain J. of Math., Volume 33, No. 1 (2003).

45. (with J.-H. Cheng) The Harnack Estimate for the Yamabe Flow on CR Manifolds of Dimension 3, Annals of Global Analysis and Geometry Vol. 21, No. 2 (2002), 111-121.

46. On the Existence of Nontrivial Extremal Metrics on Complete Noncompact Surfaces, Math. Ann. 324 (2002), 465-490.

47. Global Existence and Convergence of Solutions of the Calabi Flow on Einstein 4-Manifolds, Nagoya Math. J. Vol. 163 (2001), 193-214.

48. Compactness Theorems and the Calabi Flow on Kähler Surfaces with Stable Tangent Bundle, Math. Ann. 318 (2000), 315-340.

49. Compactness and the Calabi Flow on Kähler Surfaces with Negative Scalar Curvature, Michigan Math. J. 47-2 (2000), 217-233.








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