Analysis and geometryPh.D., 2002, Rice University
Publications:AMS Math Reviews
Web Page: http://www.math.ucdavis.edu/~qlxia/
Office: MSB 3216
Current Courses: MAT 201A
Office Hours: Monday 11-noon, or by appointment.
Research InterestsQinglan Xia 's research is devoted to a broad range of problems related to geometric measure theory. His research ranges from geometric variational problems in the intersection homology theory on singular varieties to the theory of ramified optimal transportation with branching structures, and also to very applied problems modeling the formation of the shapes in tree leaves, mud cracking and placentas. Some of his work extends to geometric analysis, combinatorial optimization, mathematical biology, and fractal geometry.
- "The formation of a tree leaf. " ESAIM Control Optim. Calc. Var., 13(2): 359-377, 2007.
- "Regularity of minimizers of quasi perimeters with a volume constraint. " Interfaces and Free Boundaries, 7(3): 339-352, 2005.
- "Interior regularity of optimal transport paths." Calculus of Variations and Partial Differential Equations, 20(3): 283-299, 2004, Full Text.
- "Intersection homology theory via rectifiable currents. " Calculus of Variations and Partial Differential Equations. 19(4): 421-443, 2004, Full Text.
- "Optimal paths related to transport problems." Communications in Contemporary Mathematics, 5(2): 251-279, 2003.
Last updated: 2008-04-21