Welcome to Qinglan Xia's Homepage






Associate Professor Email: qlxia@math.ucdavis.edu
Department of Mathematics Tel. (530)554-1196 (O)
University of California at Davis  Fax: (530)752-6635


My Research  
  • Research Interests: 
    • Geometric measure theory and its applications
    • Optimal transportation and its applications in e.g. mathematical biology, mathematical economics.
  • Publications 

  1. On the ramified optimal allocation problem. (With Shaofeng Xu). arXiv:1103.0571v1, Submitted.

  2. The exchange value embedded in a transport system. (With Shaofeng Xu). Applied Mathematics and Optimization. Vol. 62, Issue 2 (2010), 229 - 252. 
         Optimal allocation
  1. Ramified optimal transportation in geodesic metric spaces.     Adv. Calc. Var.
    2. Volume 4, Issue 3, Pages 277–307 (2011)

  2. On the transport dimension of measures. (With Anna Vershynina). SIAM J. MATH. ANAL. Vol. 41, No. 6,(2010) pp. 2407-2430.

  3. Boundary regularity of optimal transport paths.  Adv. Calc. Var. Volume 4, Issue 2, (2011), 153–174

  1. Diffusion-limited aggregation driven by optimal transportation. (With Douglas Unger). Fractals. Vol. 18, No.2 (2010), 247-253.  

  1. Numerical simulation of optimal transport paths. arXiv:0807.3723.  the Second International Conference on Computer Modeling and Simulation (ICCMS 2010). Vol 1, (2010) pp521-525. DOI: 10.1109/ICCMS.2010.30 .

  1. The geodesic problem in quasimetric spaces.Journal of Geometric Analysis: Volume 19, Issue2 (2009), Page 452-479

  2. The formation of a tree leaf. ESAIM Control Optim. Calc. Var. 13 (2007), no. 2, 359--377.

  3. An application of optimal transport paths to urban transport networks. Discrete and Continuous Dynmical Systems, Supp. Volume, 2005, 904-910.
  1. Regularity of  minimizers of quasi perimeters with a volume constraint. Interfaces and Free Boundaries. Volume 7, Issue 3, 2005, pp: 339-352

  2. Interior regularity of optimal transport paths.  Calculus of Variations and Partial Differential Equations. Vol. 20, No. 3 (2004) 283-299.

  3. Intersection homology theory via rectifiable currents.  Calculus of Variations and Partial Differential Equations.  Vol. 19, No. 4 (2004), 421-443.
  1. Optimal paths related to transport problems. Communications in Contemporary Mathematics. Vol. 5, No. 2 (2003) 251-279.

  2. 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.

  3. On the spectrum of Clifford hypersurface. (with Xu, Senlin)  Journal of Mathematical Study. Vol 29 (1996), no. 4, 5--9.  
My Teaching 
In Fall 2011, I am teaching MAT 201B (Analysis)  and 17C (Calculus for biology and Medicine)