Qikeng Lu
Office: Room , Si Yuan Building
E-Mail: luqiATmath.ac.cn
Research Interests：Lie algebras, vertex operator algebras, partial differential equations, self-dual lattices and codes
Research Summary:
Established the harmonic functions on clasical domain
Using the principal bundles to Yang-Mills fields firstly
Constant holomorphic curvature characterized unit ball
Lu's lemma introduced the analytic invariants
Got the explicit heat kernels on symmetric spaces
Computed the solution for Einstein-Yang-Mills equation
Obtained an integral representation of solution of the \bar\partial-equation
Got a Plemelj formula to the Bochner-Martinelli integral
Bergman metric dominated the Caratheodory metric
Representative Research Works:
1. 多复变函数与酉几何，数学进展, (4), 2(1956), 587-662.
2. Privalov定理的拓广，数学学报，（1）, 7(1957), 144-165. (钟同德合作).
3. Schwarz lemma and analytic invariants, Scientia Sinica, (5), 7(1958),453-504.
4. Explicit formula of the infinitesimal connection for a continuous representation of GL(n, R),Science Record, (7), 3(1959), 296-300.
5. Slit space and extremal principle, Science Record , (7), 3(1959) , 289-294.
6. Theory of harmonic functions in classical domains, Scientia Sinica, (10), 8(1959), 1031-1094. (& L.K.Hua)
7.关于可递域的一个注记，科学学报，（1），11（1961）,11-23,（与许以超合作）
8. 多复变函数引论，科学出版社，1961，vi+170页.
9. On a class of homogeneous complex manifolds, Scientia Sinica, (6), 11(1962), 723-751.
10. 典型流形与典型域，上海科学出版社，1963，iii+376页.
11. A note on the Cauchy-Fantappie formula. Scientia Sinica,(4), 14 (1965), 624-620.
12. On the complete Kaehler manifolds with constant unitary curvature, Scientia Sinica, (6),14(1965), 921-927.
13. 关于常曲率的Kaehler流形，数学学报，(2). 16(1966), 269-281.
14. 规范场与主纤维丛上的联络，物理学报(4), 23(1974), 249-263.
15. 典型时空中的运动效应和宏观红移现象，物理学报(4), 23(1974), 225-238(与邹振隆、郭汉英合作).
16.食变双星偏食光变曲线介,中国科学, (1), (1978), 71-83, (与陈建生、邹振隆合作).
17. The estimation of the intrinsic derivatives of the analytic mapping of bounded domains, Scientia Sinica, Special series II, (1979), 1-17.
18. On the Schwarz lemma of complete Kaehler manifolds, Scientia Sinica, (II), 22 (1979) , 1038-1048 (with C. Z. Chen, Siu-yuen Cheng).
19. The right-translation invariant metric and variational principles on a principal fibre bundle, Proc. of the 1980 Conference of Theoretical Particle Physics, 988-1005 (与吴咏时合作).
20. 微分几何学及其在物理学中的应用. 科学出版社, 北京, 1982.
21. A formulation of nonlinear gauge theory and its applications. Proc. 3d M.Grossmann Meeting on general Relativity, vol. I, 89-116, Sci. Press and North Holland Publ. Co.,1983; Commun. in Theory. Phys. (Beijing, China), (2), 2(1983), 1029-1038 (与郭汉英、吴可合作).
22. A Note on the extrenum of sectional curvature of a Kaehler manifold, Scientia Sinica, Series A, 27(1984), 367-374.
23. On the representative domain, Proceedings 1981 Hangzhou Conference, 199-210, Birkhaeuser, 1984.
24. The Green forms and Cauchy formulas of a Kaehler manifoldd, Chinese Quart. J.Math,2(1987), 1-12.
25. The various kernels in classical domains and classical manifolds, vol II, 199- 211,Proc. Intern. Symp. in memory of Hua Loo- keng, Sci. Press and Springer- Verlag, 1991.
26. The the theory of functions of several complex variables in China from 1949 to 1989, Contemporary Geometry, pp.53-91, Plenum Press, New York, 1991.
27. The heat kernel of the classical domain I (m,n), Proc. Mittag-Leffler Institute, chapt.25, pp. 483-506, Math. Notes, Princeton Univ. Press, 1993.
28. The heat kernels of symmetric spaces, Proc. Symposium in Pure Math., vol.54, (1993), Part II,401-409.
29. On the Cauchy-Fantappie formula and the solution of \bar{}-equation, Differential Geometry, Proc. Symposium in Honor of Prof. SU Buchin on his his 90th Birthday, pp.137-149, ed. By Gu-Hu-Xin, World Scientific, Singapore, 1993.
30. On non-linear gauge theory, Interface Between Physicx and Mathematics, ed. by W. Nahm and J. Shen, 138-153, World Scientific, Singapore, 1994.
31. The horo-hypercircle coordinate and its application, Chinese Science Bulletin, No.3, 40(1995), 92-95.
32. A matrix formulation of the complex flag manifold, Five Decades As A Mathematician and Educator (on the 80th birthday of Prof. Yung-Chou Wong), ed. by K.-Y. Chan and M.-C. Liu, 259-277, World Scientific, Singapore, 1995.
33. The real horo-hypercircle coordinate, Chinese Science Bulletin, No7, 41 (1996).
34. The horo-hypercircle coordinates and their application to the contruction of a heat kernel. Study in Advanced Math. vol.5: Singularity and Complex Geometry, ed. Qi-keng Lu, Stephen S. T. Yau and A. Libgober, 131-174, AMS/IP, 1997.
35. 典型流形与典型域，上海科技出版社，1997，iii+367.
36. The mass term in the Lagrangian of nonlinear gauge theory (to appear in Proc. Intern Conference on Frontier of Physic, Joint Meeting on Chinese Physical Societies, Shantou, 1995).
37. The Yang-Mills field on the Minkowski space, Science in China, 41 (1998), 1061-1067.
38. The unitary connections on the complex Grassmann manifold, Science in China(Series A),41(1998), 1248-1254.
39. A note on self-dual and anti-self-dual gauge field, System Science and Mathematical Science, 12 Suppl.(1999), 70-73.
40. Global geometric properties of AdS space and the AdS/CFT correspondence(joint work with Chang Zhe & Gou Hanying), Science in China, A44(6)(2001), 690-695.
41. A global solution of Einstein-Yang-Millis equations on the conformal space, Science in China, Series A, 5(2002). 343-355.
42. Global solutions of Einstein-Dirac equation on the conformal space (joint work with Wang Shikun & Wu ke), Asian J. Math., 8(2004), 1-26.
43. Hua Operator on vector bundle: Application to AdS/CFT correspondence of Dirac fields, Science in China, Ser. A Mathematics, 48(2005), 413-431.
44. On the quaternion ball and the quaternion projective space, Acta Mathematica Sinica, English Series, 15(2005), 1-10.
45. The Heisenberg group and the energy-momentem conservative law in de-Sitter spaces, Commun. Theor. Phys. (Bejing, China), 44(2005), 389-392.
46. Global solutions of Yang-Mills equation, CUBO A Mathematical Journal, 8(2006), 47-51.
47. A representation of the Lorentz spin group and its aplication, Acta Mathematica Sinica, English Series, 23(2007), 1-22 (join work with Wu Ke).
48. Holomorphic invariant forms of a bounded domain, Science in China, Serries A: Mathematics, No. 11, 51(2008),1945-1964.
49. The conjugate points of CP∞ and the zeroes of Bergman, 29B(3)(2009), 480-492.
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