Welcome to Qinglan Xia's Homepage
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Department of Mathematics Email: qlxia@math.ucdavis.edu
University of California at Davis Tel. (530)752-1084 (O), Fax: (530)752-6635

Who am I?

My Research  
These materials are based upon work supported by the National Science Foundation under Grant No.0306686, 0607107, 0710714.  Any opinions, findings and conclusions or recomendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF).
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    1. The exchange value embedded in a transport system. (With Shaofeng Xu)  arXiv:1001.5232
    2. Ramified optimal transportation in geodesic metric spaces.  arXiv:0907.5596
    3. On the transport dimension of measures. (With Anna Vershynina). SIAM J. MATH. ANAL. Vol. 41, No. 6,(2010) pp. 2407-2430
    4. Diffusion-limited aggregation driven by optimal transportation. (With Douglas Unger).  Accepted by the Fractals journal (2009).
    5. Numerical simulation of optimal transport paths. arXiv:0807.3723. To appear on the Proceedings of the 2nd International Conference on Computer Modeling and Simulation (ICCMS 2010)
    6. The geodesic problem in quasimetric spaces. Journal of Geometric Analysis: Volume 19, Issue2 (2009), Page 452-479.
    7. The formation of a tree leaf. ESAIM Control Optim. Calc. Var. 13 (2007), no. 2, 359--377.
    8. Regularity of  minimizers of quasi perimeters with a volume constraint. Interfaces and Free Boundaries. Volume 7, Issue 3, 2005, pp: 339-352
    9. Boundary regularity of optimal transport paths. 
    10. An application of optimal transport paths to urban transport networks. Discrete and Continuous Dynmical Systems, Supplement Volume, 2005, pp 904-910.
    11. Interior regularity of optimal transport paths.  Calculus of Variations and Partial Differential Equations. Vol. 20, No. 3 (2004) 283-299.
    12. Intersection homology theory via rectifiable currents.  Calculus of Variations and Partial Differential Equations.  Vol. 19, No. 4 (2004), 421-443.
    13. Optimal paths related to transport problems. Communications in Contemporary Mathematics. Vol. 5, No. 2 (2003) 251-279.
    14. Conformal deformation of a closed Riemannian submanifold to a minimal submanifold. (with Xu, Senlin)  Journal of Mathematical Study, Vol 31 (1998), no. 2, 109--115. A summary version is also published on  Chinese Science Bulletin,  Vol 43 (1998), no. 6, 527.
    15. On the spectrum of Clifford hypersurface. (with Xu, Senlin)  Journal of Mathematical Study. Vol 29 (1996), no. 4, 5--9.  
My Teaching 
 In Fall 2009, I am teaching MAT 125A (Real Analysis).