Qinglan Xia's Publications

Published/Accepted (commentary remarks about these papers may be found HERE.)
  1. Ramified optimal transportation in geodesic metric spaces.  arXiv:0907.5596.  Accepted by Advances in Calculus of Variations. (2010)
  2. The exchange value embedded in a transport system. (With Shaofeng Xu)  arXiv:1001.5232. To appear in Applied Mathematics and Optimization (2010).
  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). Fractals. Vol. 18, No.2 (2010) 1-7.  
  5. 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 .
  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. An application of optimal transport paths to urban transport networks. Discrete and Continuous Dynmical Systems, Supp. Volume, 2005, 904-910.

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

  11. Intersection homology theory via rectifiable currents.  Calculus of Variations and Partial Differential Equations.  Vol. 19, No. 4 (2004), 421-443.

  12. Optimal paths related to transport problems. Communications in Contemporary Mathematics. Vol. 5, No. 2 (2003) 251-279.

  13. 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.

  14. On the spectrum of Clifford hypersurface. (with Xu, Senlin)  Journal of Mathematical Study. Vol 29 (1996), no. 4, 5--9.  

Submitted
  1. Boundary regularity of optimal transport paths. Submitted to Advances in Calculus of Variations.
Working in progress
  1. River Channel Networks modelled by optimal transport paths.  
  2. A mathematical model of placentals using optimal transport paths. 
  3. Flow of surfaces driven by optimal transportation
  4. On optimal fractals
  5. On the formation of trees
  6. Ramified optimal transportation in metric spaces
  7. Optimal transportation of rectifiable currents
  8. Optimal transportation of varifolds