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# Lee, Hsuan-Pei

 Dr. Lee used to work in complex analysis of several variables, especially in studying the solvability  of $\bar{\partial}_b$ operators. A few years ago, she and C. H. Chang  were introduced by works of B. Gaveau, P. Greiner et al. to the subRiemannian geometry, and they have worked on this subject since then. They  went through a fairly thorough analysis of the geometry for the step two Grusin operator, obtained the geodesics, complex action function, heat kernel as well as the asymptotic behavior of the heat kernel near the critical points of the action function. Then by carefully choosing the path of integration, they were able to give an elementary proof of the positivity of the heat kernel for the 3-dimensional Heisenberg group. They have been also working on the Engel group, which is a step 3 Carnot group. Although the formulas for the geodesics as well as the complex action function have been obatined, a deeper analysis on the obtained formulas is needed to construct the heat kernel. Email : hplee AT math.sinica.edu.tw Phone:+886 2 2368-5999 ext. 634 Fax: +886 2 2368-9771

### Publications :

 1 (with Chang, C.-H., Chang, D.-C., Greiner, P.) The positivity of the heat kernel on Heisenberg group, Analysis and Applications , 11(2013), no. 5, 0-0 2 Tame measures on certain compact sets, Proceedings of AMS , 80(1980), 61-67 3 (with John Wermer) Orthogonal measures for subsets of the boundary of the ball in $C^{2}$, Annals of Mathematics Studies , 100(1981), 277-289 4 (with C.H. Chang and A.N. Wang) Extremal analytic discs and the chains., Chinese J. Math. , 13(1985), 239-255 5 (with C. H. Chang, J. H. Cheng, A. N. Wang) Examples of spiralling chains, report to NSC 1985., (1985), 0-0 6 (with C.H. Chang, M.C. Hu) Extremal analytic discs with prescribed boundary data, Transaction of A.M.S. , 310(1988), 355-369 7 (with C.H. Chang) 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 (1988), 193-203 8 (with C. H. Chang) A counterexample to Slodkowski's theorem in $C^n(n\geq 3)$, (1989), 0-0 9 (with C. H. Chang) Notes on CR manifolds, preliminnary report to NSC 1990., (1990), 0-0 10 (with C. H. Chang, I. L. Hwang) Extending CR functions and solving $\overline\partial_b$ on some open CR manifolds, report to NSC 1991., (1991), 0-0 11 (with C. H. Chang) Semi-global solutions of $\overline\partial_b$ with $L^p$ $(1\leq p\leq \infty)$ bounds on strongly pseudoconvex real hyper surfaces in $C^n(n\geq 3)$, Publicacions Matemàtiques , 43(1999), 535-570 12 (with C. H. Chang) $L^p$ estimates for $\overline\partial$ in some weakly pseudoconvex domains in $C^n$, Mathematische Zeitschrift , 235(2000), 379-404 13 (with C. H. Chang) Hartogs theorem for CR functions, Bull. Inst. Math. Academia Sinica , 32(2004), 221-227 14 (with C. H. Chang) Hartogs theorem for forms: solvability of Cauchy-Riemann operator at critical degree, Ann. Scuola Norm. Sup. Pisa Cl. Sci. , 5(2006), 21-37 15 (with C. H. Chang) Hartogs theroem for forms: analyticity of singular sets, (2009), 0-0(in preparation) 16 (with C. H. Chang, D. C. Chang, B. Gaveau, P. Greiner) Geometric analysis on a step 2 Grusin operator, Bulletin of the Institute of Mathematics,Academia Sinica(New Series) , 4(2009-06), no. 2, 119-188