Welcome to Qinglan Xia's Homepage

My Research
- Research Interests:
- Geometric measure theory and its
applications
- Optimal transportation and its applications in e.g.
mathematical biology, mathematical economics.
- Ramified optimal transportation with payoff on the boundary (With Shaofeng Xu). https://arxiv.org/pdf/2009.07812
- The existence of minimizers for an isoperimetric problem with
Wasserstein penalty term in unbounded domains (With Bohan Zhou). Advances in Calculus of Variations, vol. , no. , 2021, pp. 000010151520200083. https://doi.org/10.1515/acv-2020-0083
- On the Curvature of Metric Triples. https://arxiv.org/pdf/2109.01602.pdf
- A fractal shape optimization problem in branched transport (With Paul Pegon, Filippo Santambrogio). Journal de Mathématiques Pures et Appliquées (2018)
https://doi.org/10.1016/j.matpur.2018.06.007
- Generalized Moran sets generated by step-wise adjustable iterated function systems (With Tynan Lazarus). https://arxiv.org/pdf/1707.08634.pdf
- 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.
- 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)
- Transport
efficiency of the human placenta. (With Carolyn Salafia). Journal of Coupled Systems and Multiscale Dynamics. 2, 1-8 (2014)
- Optimal
transport and placental function. (With Carolyn Salafia and Simon
Morgan). The proccedings of the AMMCS 2013 conference.
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On landscape functions associated with
transport paths. Discrete and
Continuous Dynamical Systems - Series A, Vol. 34, No. 4, (2014).
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On
the ramified optimal allocation problem. (With Shaofeng
Xu). arXiv:1103.0571v1,
Networks and Heterogeneous Media
p591 - 624, Volume 8, Issue 2, June 2013.
- The
exchange
value embedded in a transport system. (With Shaofeng
Xu). Applied
Mathematics and
Optimization. Vol. 62, Issue 2 (2010), 229 - 252.
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Ramified
optimal transportation in geodesic metric spaces.
Adv. Calc.
Var.
Volume 4, Issue 3, Pages 277–307 (2011) -
On
the transport dimension of measures. (With Anna Vershynina). SIAM J. MATH. ANAL. Vol. 41, No.
6,(2010) pp. 2407-2430.
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Boundary
regularity of optimal transport paths. Adv. Calc. Var.
Volume 4, Issue 2, (2011), 153–174
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Diffusion-limited
aggregation driven by optimal transportation. (With Douglas
Unger). Fractals. Vol.
18, No.2 (2010), 247-253.
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Numerical
simulation of optimal transport paths. arXiv:0807.3723.
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- The
geodesic problem in quasimetric spaces.Journal of Geometric Analysis:
Volume 19, Issue2 (2009), Page 452-479
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The
formation of a tree leaf. ESAIM Control Optim. Calc. Var.
13 (2007), no. 2, 359--377.
- An
application of optimal transport paths to urban transport networks.
Discrete
and
Continuous Dynmical Systems, Supp. Volume, 2005, 904-910.
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- Regularity
of minimizers of quasi perimeters with a
volume constraint. Interfaces
and Free Boundaries. Volume 7, Issue 3, 2005, pp: 339-352
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Interior
regularity of optimal transport paths. Calculus
of Variations and Partial Differential Equations. Vol. 20,
No.
3
(2004) 283-299.
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Intersection
homology theory via rectifiable currents. Calculus
of Variations and Partial Differential Equations.
Vol. 19,
No.
4 (2004), 421-443.
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- Optimal
paths related to transport problems. Communications in
Contemporary Mathematics.
Vol. 5, No. 2 (2003) 251-279.
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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.
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On the spectrum of
Clifford
hypersurface. (with Xu,
Senlin) Journal
of
Mathematical Study. Vol 29 (1996), no. 4,
5--9.
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My
Teaching
In
Winter 2019, I will teach the course MAT 127B: Real Analysis
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