• cheng$\color{red}{@}$math.sinica.edu.tw
• +886 2 2368-5999 ext. 631
• +886 2 2368-9771

• 幾何分析
• 低維拓樸
• 多複變幾何

• Ph.D. in Mathematics Univ. of Notre Dame (1983/5)
• M.S. 清華大學 (1979/6)
• B.S. 台灣大學 (1975/6)

• Research Fellow Institute of Mathematics, Academia Sinica, R.O.C. 1988
• Associate Research Fellow Institute of Mathematics, Academia Sinica, R.O.C. 1983

• 科技部110年度傑出特約研究員, 2021
• Ministry of Education Academic Award, 2019-12
• Academic Award of Taiwan Mathematical Society, 2017-12
• NSC distinguished research awards, 1990, 1992

1. (with Malchiodi A., Yang P.) "On the Sobolev quotient of three-dimensional CR manifolds" , Revista Matematica Iberoamericana , to appear. (arXiv: 1904.04665)
2. (with C.-H. Chang, I-H. Tsai) "Correction to : Theta functions and adiabatic curvature on an elliptic curve" , The Journal of Geometric Analysis , 32, 208 (7), 2022-07. (https://doi.org/10.1007/s12220-022-00944-w)
3. (with Chang C.-H., Tsai I-H.) "Theta functions and adiabatic curvature on an elliptic curve" , The Journal of Geometric Analysis , 32, 84 (3), 2022-03. (https://doi.org/10.1007/s12220-021-00774-2)
4. (with Hung-Lin Chiu) "Positive mass theorem and the CR Yamabe equation on 5-dimensional contact spin manifolds" , Advances in Mathematics , 404 (108446), 50 pages-, 2022. (https://doi.org/10.1016/j.aim.2022.108446)
5. (with Chiu H.-L., Ho P. T.) "Connected sum of CR manifolds with positive CR Yamabe constant" , The Journal of Geometric Analysis , 31 (1), 298-311, 2021.
6. "微分幾何學--重力研究的好幫手" , 數學傳播 , 44 (4), 27-33, 2020. (第176期)
7. "Submanifolds in Cauchy Riemann Geometry" , Journal of Mathematical Study , 53 (4), 436-470, 2020.
8. (with Chiu H.-L.) "Connected sum of spherical CR manifolds with positive CR Yamabe constant" , The Journal of Geometric Analysis , 29 (4), 3113-3123, 2019.
9. (with Marugame T., Matveev V.S., Montgomery R.) "Chains in CR geometry as geodesics of a Kropina metric" , Advances in Mathematics , 350, 973-999, 2019.
10. (with Case J.S., Yang P.) "An integral formula for the Q-prime curvature in 3-dimensional CR geometry" , Proceedings of AMS , 147, 1577-1586, 2019.
11. (with Hsiao C.-Y., Tsai I-H.) "Heat kernel asymptotics, local index theorem and trace integrals for CR manifolds with $S^1$ action" , Memoires de la SMF , 162, 2019. (152 pages)
12. (with Yang P., Zhang Y.) "Invariant surface area functionals and singular Yamabe problem in 3-dimensional CR geometry" , Advances in Mathematics , 335, 405-465, 2018.
13. (with Chiu H.-L., Hwang J.-F., Yang P.) "Umbilicity and characterization of Pansu spheres in the Heisenberg group" , Journal fur die reine und angewandte Mathematik (738), 203-235, 2018.
14. (with Chiu H.-L., Hwang J.-F., Yang P.) "Strong Maximum principle for mean curvature operator on subriemannian manifolds" , Math. Annalen , 372, 1393-1435, 2018.
15. "Contact 𝑠𝑝𝑖𝑛^{𝑐} structure, embeddability of CR structure, and positivity of the mass" , Proceedings of the Sixth International Congress of Chinese Mathematicians. Vol. II, Adv. Lect. Math. (ALM), vol. 37, Int. Press, Somerville, MA , 23-35, 2017.
16. (with Malchiodi A., Yang P.) "A positive mass theorem in three dimensional Cauchy-Riemann geometry" , Advances in Mathematics , 308, 276-347, 2017.
17. (with Chiu H.-L., Hwang J.-F., Yang P.) "Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group" , Calculus of Variations and Partial Differential Equations , 55 (3), 2016-06.
18. (with 夏杼,何南國) "有朋自遠方來--專訪Nigel Hitchin教授" , 數學傳播 , 39 (4), 3-16, 2015-12.
19. "Flows and a tangency condition for embeddable CR structures in dimension 3" , Methods and Applications of Analysis , 21 (3), 337-356, 2014.
20. (with Hwang J.-F.) "Uniqueness of generalized $p$-area minimizers and integrability of a horizontal normal in the Heisenberg group" , Calculus of Variations and PDEns , 50, 579-597, 2014. (published online: 29 June 2013)
21. (with Chiu H.-L., Yang P.) "Uniformization of spherical CR manifolds" , Advances in Mathematics , 255, 182-216, 2014.
22. (with 劉太平, 蔡忠潤) "有朋自遠方來--專訪Clifford Taubes教授" , 數學傳播 , 37 (1), 3-14, 2013-03.
23. (with Malchiodi A., Yang P.) "A positive mass theorem in three dimensional Cauchy-Riemann geometry" , Extended abstract Fall 2013, Research Perspectives CRM, Barcelona , 2013. (editors: Maria del Mar Gonzalez, Paul C. Yang, etc.)
24. (with Jenn-Fang Hwang, Andrea Malchiodi, Paul Yang) "A Codazzi-like equation and the singular set for $C^{1}$ smooth surfaces in the Heisenberg group" , Journal fur die reine und angewandte Mathematik , 671, 131-198, 2012.
25. (with Jenn-Fang Hwang) "Variations of generalized area functionals and p-area minimizers of bounded variation in the Heisenberg group" , Bulletin of the Institute of Mathematics, Academia Sinica, New Series , 5 (4), 369-412, 2010.
26. (with 劉太平, 江孟蓉) "有朋自遠方來--專訪Kenji Fukaya教授" , 數學傳播 , 33 (3), 3-12, 2009-09.
27. "The prescribed p-mean curvature equation of low regularity in the Heisenberg group" , Science in China, Series A , 52 (12), 2604-2609, 2009. (2007 International Conference on Several Complex Variables and Complex Geometry, May 28-31, 2007, Xiamen.)
28. (with Jenn-Fang Hwang!Paul Yang) "Regularity of $C^{1}$ smooth surfaces with prescribed p-mean curvature in the Heisenberg group" , Math. Annalen , 344 (1), 1-35, 2009.
29. "Surfaces of prescribed p-mean curvature in the Heisenberg group" , Proceedings of the 4th ICCM , II, 40-58, 2007. (Dec.17-22, Hangzhou, ed. L. Ji, K. Liu, L. Yang, and S.T. Yau.)
30. (with Shu-Cheng Chang ! Hung-Lin Chiu) "A fourth order curvature flow on a CR 3-manifold" , Indiana Univ. Math. J. , 56, 1793-1826, 2007.
31. (with Jenn-Fang Hwang ! Paul Yang) "Existence and uniqueness for p-area minimizers in the Heisenberg group" , Math. Annalen , 337, 253-293, 2007.
32. (with 葉永南，周文賢) "有朋自遠方來---專訪Gyula O. H. Katona教授" , 數學傳播 , 30 (1), 15-24, 2006.
33. "The mean curvature equation in pseudohermitian geometry" , Contemporary Mathematics , 400, 89-94, 2006.
34. (with Jenn-Fang Hwang!Andrea Malchiodi!Paul Yang) "Minimal surfaces in pseudohermitian geometry" , Annali della Scuola Normale Superiore di Pisa Classe di Scienze V , 4 (1), 129-177, 2005.
35. (with Jenn-Fang Hwang) "Properly embedded and immersed minimal surfaces in the Heisenberg group" , Bull. Aus. Math. Soc. , 70, 507-520, 2004.
36. (with Hung-Lin Chiu) "Monopoles and contact 3-manifolds. Quademi di Matematica, Selected Topics in Cauchy-Riemann Geometry, ed. Sorin Dragomir, 9(2003), 99-123; math. DG/9905066." , 2003.
37. "Deformation of fillable CR structures, preprint; math.DG/0202051." , 2002.
38. (with Shu-Cheng Chang) "The Harnack estimate for the Yamabe flow on CR manifolds of dimension 3, Annals of Global Analysis and Geometry, 21(2002), 111-121; math. DG/0003197." , 2002.
39. "淺談場量子化與低維拓樸." , 數學傳播 , 25 (4), 4-7, 2001-12.
40. "Rick Schoen, Yamabe 問題與正質量定理." , 數學傳播 , 24 (4), 63-67, 2000-12.
41. (with 李瑩英, 蔡宜洵) "有朋自遠方來 ---Rick Schoen 訪談紀要." , 數學傳播 , 24 (4), 58-62, 2000-12.
42. "Contact topology and CR geometry in three dimensions. Proceedings of the 3rd Asian Mathematical Conference 2000 (Quezon City, Philippines) ed. T. Sunada, P. W. Sy, Yang Lo (2002), 70-80; math.SG/0106071." , 2000/2002.
43. "Cauchy-Riemann geometry and contact topology in three dimensions. Proc. Natl. Sci. Counc., ROC(A), 24(2000), 87-94; math. DG/0003211." , 24, 87-94, 2000.
44. "Rigidity of automorphisms and spherical CR structures. Proc. Amer. Math. Soc., 128(2000), 1825-1832; math. DG/9806108." , Proc. Amer. Math. Soc. , 128, 1825-1832, 2000.
45. (with I-Hsun Tsai) "Deformation of spherical CR structures and the universal Picard variety. Commun. in Anal. And Geom., 8(2000), 301-346; math. DG/9807035." , Commun. in Anal. And Geom. , 8, 301-346, 2000.
46. "The geometry of Cauchy-Riemann manifolds in dimension three, Proceedings of the second Asian mathematical conference, Suranaree University of Technology, Nakhon Ratchasima, Thailand, (Oct. 17-20, 1995), ed. S.Tangmanee and E. Schulz (1998), 201-208." , 201-208, 1998.
47. (with John M. Lee) "A local slice theorem for 3-dimensional CR structures" , Amer. J. Math. , 117, 1249-1298, 1995.
48. "Some applications of Cartan's theory on three-dimensional Cauchy-Riemann geometry" , Math. Zeit. , 218, 527-548, 1995.
49. (with Shuenn-Jyi Sheu) "Brownian motion on pseudohermitian manifolds" , incomplete draft , 1994.
50. "Cauchy-Riemann geometry and contact topology on three-manifolds, Proceedings of conference on the 29th annual meeting of ROC Math. Soc., National Chiao-Tung University, Hsinchu, Taiwan, (Dec. 3-4, 1993), 105-111." , 105-111, 1993.
51. "On embeddable CR 3-manifolds" , draft , 1992.
52. "淺談Jones-Witten理論及Floer同調群." , 數學傳播 , 15 (1), 12-22, 1991-03.
53. "Curvature functions for the sphere in pseudohermitian geometry" , Tokyo J. Math. , 14, 151-163, 1991.
54. (with John M. Lee) "The Burns-Epstein invariant and deformation of CR structures" , Duke Math. J. , 60, 221-254, 1990.
55. "Deforming CR structures in the direction of Cartan tensor, Proceedings of the 1989 Conference on nonlinear analysis, Academia Sinica, Taipei, R.O.C. (June 19-24, 1989), 17-22, World Scientific." , 1989.
56. "Chain-preserving diffeomorphisms and CR equivalence" , Proceedings of AMS , 103, 75-80, 1988.
57. "On the curvature of CR structures and its covariant derivatives" , Math. Zeit. , 196, 203-209, 1987.
58. "Graded Lie algebras of the second kind" , Transactions of AMS , 302, 467-488, 1987.
59. "On the second fundamental form of algebraic hypersurfaces" , Bulletin of IMAS , 10, 25-34, 1982.
60. "An integral formula on the scalar curvature of algebraic manifolds" , Proceedings of AMS , 81, 451-454, 1981.
61. "CR umbilicity for certain class of real hypersurfaces in $C^{n+1}$" , draft
62. (with C.H. Chang, H.P. Lee and A.N. Wang) "Examples of spiralling chains" , draft
63. "CR structures for a family of homogeneous spaces" , draft