退休研究人員 |   張清煇
聯絡資訊
  • pino$\color{red}{@}$math.sinica.edu.tw
  • +886 2 2368-5999 ext. 635
  • +886 2 2368-9771
研究專長
  • 偏微分方程
學歷
  • Ph.D. Purdue University (1982)
  • B.S. 台灣大學 (1974)
相關連結

經歷
  • Research Fellow Institute of Mathematics, Academia Sinica, R.O.C. 2007 - Present
  • Associate Research Fellow Institute of Mathematics, Academia Sinica, R.O.C. 1983 - 2007
  • Member Institute of Adavance Study 1982 - 1983

研究簡介

Dr. Chang's research interests are linear partial differential equations and analysis of several complex variables. A couple years ago, He and H. P. Lee started to work on geometric analysis in subRiemannian geometry. This topic is closely connected with Hörmander's work on sums of squared vector fields which are bracket generating. One goal is to construct the heat kernel of the subLaplacian in this geometry. The approach is to apply the geometric mechanics ( i.e. Hamiltonian mechanics) method which has been used in the Riemannian geometry case. Together with D. C. Chang, B. Gaveau, P. Greiner and H. P. Lee they got a quite complete result for step two Grusin operator in 2009. Then by a careful study of the integration path of the heat kernel, an elementary proof on the positivity of the heat kernel on 3-dimensional Heisenberg group was obtained. In subRiemannian geometry the Carnot groups play the role as linear spaces do in Riemannian geometry. He and H. P. Lee have been working on Engel group ( a step 3 Carnot group). They obtained formulas of the geodesics as well as the complex action function which have been proved to satisfy the generalized Hamilton-Jacobi equation.


部分著作目錄
  1. (with Chang, D-.C., Greiner, P., Lee, H.-P.) "The positivity of the heat kernel on Heisenberg group" , Analysis and Applications , 11 (5), 2013.
  2. (with D.C.Chang, B.Gaveau, P.Greiner, H.P.Lee) "Geometric analysis on a step 2 Grusin operator" , Bulletin of the Institute of Mathematics,Academia Sinica(New Series) , 4 (2), 119-188, 2009-06.
  3. (with H.P. Lee) "Hartogs theorem for forms: annalyticity of singular sets, in preparation" , 2009.
  4. (with H. P. Lee) "Hartogs theorem for forms: solvability of Cauchy-Riemann operator at critical degree" , Ann. Scuola Norm. Sup. Pisa Cl. Sci. , 5, 21-37, 2006.
  5. (with H. P. Lee) "Hartogs theorem for CR functions" , Bull. Inst. Math. Academia Sinica , 32, 221-227, 2004.
  6. (with Y. S. Chow, Z. Wang) "On the asymptotic behavior of heating times" , Analysis and Applications , 1 (4), 429-432, 2003.
  7. (with H. P. Lee) "$L^p$ estimates for $\overline{\partial}$ in some weakly pseudoconvex domains in $C^{n}$''" , Mathematische Zeitschrift , 235, 379-404, 2000.
  8. (with H. P. Lee) "Semi-global solutions of tangential CR operators with $L^p$ $(1\leq p\leq \infty)$ bounds on strongly pseudoconvex real hypersurfaces in $C^n(n\geq 3)$" , Publicacions Matematiques , 43, 535-570, 1999.
  9. (with I. L. Hwang, H. P. Lee) "Extending CR functions and solving $\overline\partial_b$ on some open CR manifolds, preprint, report to NSC 1991." , 1991.
  10. (with H. P. Lee) "Notes on CR manifolds, preliminnary report to NSC 1990." , 1990.
  11. (with Lee, H.-P.) "Explicit solutions for some extremal analytic discs of the domain $D= \{Z \in {C}^n : \sum_{1}^n |Z_j |^{2m_j} <1, m_j \in N\}$" , Several Complex Variables: Proceedings of the Mittag-Leffer Institute, 1987-1988(Mathematical Notes, no. 38), Princeton Univ. Press , 193-203, 1990.
  12. (with H. P. Lee) "A counterexample to Slodkowski's theorem in $C^n(n\geq 3)$ , report to NSC 1989." , 1989.
  13. (with M.C. Hu, H. P. Lee) "Extremal analytic discs with prescribed boundary data" , Trans. A.M.S. , 310, 355-369, 1988.
  14. (with H. P. Lee, J. H. Cheng, A. N. Wang) "Examples of spiralling chains, report to NSC 1985." , 1985.
  15. (with H. P. Lee, A.N. Wang) "Extremal analytic discs and the chains" , Chinese J. Math., 13(1985), 239-255. , 13, 239-255, 1985.
  16. "Hypoanalyticity with vanishing Levi form" , Bulletin, Institute of Math., Academia Sinica , 13, 123-136, 1985.
  17. (with M.S. Baouendi, F. Treves) "Microlocal hypoanalyticity and extension of CR functions" , J. Differential Geometry, 18(1983), 331-392. , 18, 331-392, 1983.