# Qinglan Xia

Professor

Analysis and geometry

Ph.D., 2002, Rice UniversityWeb Page: http://www.math.ucdavis.edu/~qlxia/

Email: qlxia@math.ucdavis.edu

Office: MSB 3216

Current Courses: MAT 21C, MAT 206

Office Hours: Mon/Thur 1:30~2:30pm (21C); Wed 1:30~2:30p (206)

Phone: 530-754-0493

### Research Interests

Qinglan 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.

### Selected Publications

- "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*