Jie Qing is interested in nonlinear analysis, harmonic analysis, and partial differential equations (systems) with applications to differential geometry, complex geometry and mathematical physics. Most recently, Professor Qing has continued his research on the study of singular behavior of harmonic maps and the heat flow for harmonic maps. He continues his research on the study of the Ginzburg-Landau problem and continues to be involved in the study of the geometry of conformally covariant differential operators on 4-manifolds.
Main publications:
J. Qing: A priori estimates for positive solutions of semi-linear elliptic systems. J. Partial Differential Equations, Vol. q, No. 2, Series A (1988), 61–70.
J. Qing: Regularity of the minima of certain variational integrals. Preprint (in Chinese).
J. Qing: Remarks on the Dirichlet problem for harmonic maps from disc into 2-sphere. Proc. Royal Soc. Edinburgh 122A (1992), 63–67.
J. Qing: Dirichlet problem for harmonic maps from disc into Kahler manifolds. J. Lon. Math Society (2) 47 (1993), 182–192.
J. Qing: Multiple olutions of the Dirichlet problem for harmonic maps from disc into 2-sphere manuscripta Math. 77 (1992), 435–446.
J. Qing: Boundary regularity of weakly harmonic maps from surfaces. J. Functional Analysis 11 (1993), 458–466.
J. Qing: On the singularity of the heat flow for harmonic maps from surfaces into spheres. Comm in Anal. and Geo. Vol 3 (1995), No. 2, 297–315.
J. Qing: Renormalized energy for Ginzburg–Landau vortices on closed surfaces. To appear in Mathema-tische Zeitschrift.
J. Qing: Functional determinants on manifolds with boundary (joint with Alice Chang, research announcement), To appear in Math. Research Letter.
J. Qing: Zeta functional determinants on manifolds with boundary I - the formula (joint with Alice Chang). Submitted to Journal Funct. Anal.
J. Qing: Bubbling of the heat flows for harmonic maps from surfaces (joint with Gang Tian). Comm. Pure and Appl. Math. L (1997), 295–310
J. Qing: Harmonic maps from surfaces. Lecture notes in the proceeding of the second workshop of non-linear functional analysis and its applications in PDE at ICTP of Italy in 1997.
J. Qing: Ginzburg-Landau vortices and Mandelstam diagrams. Submitted to Pacific Journal of Math.
P. Yang, J. Qing, S.-Yu. Chang, “On the renormalized volumes for conformally compact Einstein manifolds”, CMFD, 17 (2006), 129–142; Journal of Mathematical Sciences, 149:6 (2008), 1755–1769
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