Welcome to Qinglan Xia's Homepage

Professor

Email: qlxia@ucdavis.edu

Department of Mathematics

Tel. (530)754-0493 (O)

University of California at Davis

Fax: (530)752-6635

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My Research

Research Interests

Publications

  1. Telecommuting in an Economy with Transport Networks. (With Shaofeng Xu) Submitted to Journal of Mathematical Economics.
  2. Branching Pattern Modeling: A Geometric Measure Theory Approach. Proceedings of the 2025 Westlake Winter School in Geometric Measure Theory , to appear.
  3. Transport multi-paths with capacity constraints (With Haotian Sun). Journal of Mathematical Analysis and Applications. Volume 550, Issue 1, 2025, 129499. DOI: 10.1016/j.jmaa.2025.129499
  4. Map-compatible decompositions of transport paths (With Haotian Sun). Published online in Communications in Contemporary Mathematics (2026), article 2650076. DOI: 10.1142/S0219199726500768. arXiv:2310.03825.
  5. Partial Plateau's Problem with H-mass (With Enrique Alvarado). Calculus of Variations and Partial Differential Equations. Vol. 64, No. 13 (2025). https://doi.org/10.1007/s00526-024-02845-y
  6. Ramified optimal transportation with payoff on the boundary (With Shaofeng Xu). SIAM J. MATH. ANAL. vol 55, No.1 (2023) pp. 186-209. https://arxiv.org/pdf/2009.07812
  7. The existence of minimizers for an isoperimetric problem with Wasserstein penalty term in unbounded domains (With Bohan Zhou). Advances in Calculus of Variations, vol. 16, no.1, 2023, pp. 1-15. https://doi.org/10.1515/acv-2020-0083
  8. On the Curvature of Metric Triples. in Proceedings of the International Consortium of Chinese Mathematicians 2019, S.-Y. Cheng, S. Li, and S.-T. Yau (eds.), International Press, Somerville, MA, 2024. https://arxiv.org/pdf/2109.01602
  9. A fractal shape optimization problem in branched transport (With Paul Pegon, Filippo Santambrogio). Journal de Mathématiques Pures et Appliquées, Vol 123, March 2019, pp 224-269. https://doi.org/10.1016/j.matpur.2018.06.007
  10. Generalized Moran sets generated by step-wise adjustable iterated function systems (With Tynan Lazarus). https://arxiv.org/pdf/1707.08634.pdf
  11. Motivations, ideas, and applications of ramified optimal transportation. ESAIM: Mathematical Modelling and Numerical Analysis. Volume 49, Number 6, November-December 2015. Special Issue - Optimal Transport. pp 1791 - 1832.
  12. Human Placentas, Optimal Transportation and High-risk Autism Pregnancies. (With Carolyn Salafia, etc.). Journal of Coupled Systems and Multiscale Dynamics. 4(4), 260-270. (2016)
  13. Transport efficiency of the human placenta. (With Carolyn Salafia). Journal of Coupled Systems and Multiscale Dynamics. 2, 1-8 (2014)
    Optimal transport path for a human placenta; see Transport efficiency of the human placenta
  14. Optimal transport and placental function. (With Carolyn Salafia and Simon Morgan). The proccedings of the AMMCS 2013 conference.
  15. On landscape functions associated with transport paths. Discrete and Continuous Dynamical Systems - Series A, Vol. 34, No. 4, (2014).
  16. On the ramified optimal allocation problem. (With Shaofeng Xu). arXiv:1103.0571v1, Networks and Heterogeneous Media p591 - 624, Volume 8, Issue 2, June 2013.
  17. The exchange value embedded in a transport system. (With Shaofeng Xu). Applied Mathematics and Optimization. Vol. 62, Issue 2 (2010), 229 - 252.
  18. Ramified optimal transportation in geodesic metric spaces. Adv. Calc. Var. Volume 4, Issue 3, Pages 277–307 (2011)
  19. On the transport dimension of measures. (With Anna Vershynina). SIAM J. MATH. ANAL. Vol. 41, No. 6,(2010) pp. 2407-2430.
  20. Boundary regularity of optimal transport paths. Adv. Calc. Var. Volume 4, Issue 2, (2011), 153–174
  21. Diffusion-limited aggregation driven by optimal transportation. (With Douglas Unger). Fractals. Vol. 18, No.2 (2010), 247-253.
    Diffusion-limited aggregation; see Diffusion-limited aggregation driven by optimal transportation
  22. Numerical simulation of optimal transport paths. 2010 Second International Conference on Computer Modeling and Simulation, Sanya, China, 2010, pp. 521-525, doi: 10.1109/ICCMS.2010.30. arXiv:0807.3723.
  23. The geodesic problem in quasimetric spaces.Journal of Geometric Analysis: Volume 19, Issue2 (2009), Page 452-479
  24. The formation of a tree leaf. ESAIM Control Optim. Calc. Var. 13 (2007), no. 2, 359–377.
    Mathematical leaf model; see The formation of a tree leafNumerically generated leaf and vein network; see The formation of a tree leaf
  25. An application of optimal transport paths to urban transport networks. Discrete and Continuous Dynmical Systems, Supp. Volume, 2005, 904-910.
  26. Regularity of minimizers of quasi perimeters with a volume constraint. Interfaces and Free Boundaries. Volume 7, Issue 3, 2005, pp: 339-352
    Mud cracks; see Regularity of minimizers of quasi perimeters with a volume constraint
  27. Interior regularity of optimal transport paths. Calculus of Variations and Partial Differential Equations. Vol. 20, No. 3 (2004) 283-299.
  28. Intersection homology theory via rectifiable currents. Calculus of Variations and Partial Differential Equations. Vol. 19, No. 4 (2004), 421-443.
  29. Optimal paths related to transport problems. Communications in Contemporary Mathematics. Vol. 5, No. 2 (2003) 251-279.
    Branched optimal transport network with two source points; see Optimal paths related to transport problems
  30. 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.
  31. On the spectrum of Clifford hypersurface. (with Xu, Senlin) Journal of Mathematical Study. Vol 29 (1996), no. 4, 5--9.