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研究員 |   張清煇

 



聯絡資訊
  • Email : pino AT math.sinica.edu.tw
  • Phone:+886 2 2368-5999 ext. 635
  • Fax:    +886 2 2368-9771
  相關連結

學歷
  • Ph.D. Purdue University (1982)
  • B.S. 台灣大學 (1974)
  研究專長
  • 偏微分方程

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 List ↓

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