Xiaodan Zhou

Prof Xiaodan Zhou
Xiaodan Zhou
Assistant Professor
Ph.D., University of Pittsburgh, 2016
B.S., Beijing Normal University, 2011

Professional Experience

  • Assistant Professor, OIST, 2020 to Present
  • Post-Doctoral Scholar, Worcester Polytechnic Institute, 2016-2020
  • Teaching/Research Assistant, University of Pittsburgh, 2011-2016

Grants and Awards

Select Publications

  • Equivalence of solutions of eikonal equation in metric spaces, (joint with Q. Liu and N. Shanmugalingam), J. Differential Equations 272 (2021), 979–1014.

  • Functions of bounded variation on complete and connected one-dimensional metric spaces, (with P. Lahti), Int. Math. Res. Not.IMRN 2021, no. 20, 15412–15443.

  • Horizontal convex envelope in the Heisenberg group and applications to sub-elliptic equations, (with Q. Liu),  Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 22 (2021), no. 4, 2039–2076.

  • Absolutely continuous functions on compact and connected one-dimensional metric spaces, Ann. Acad. Sci. Fenn. Math. Volumen 44, (2019), 281-291.

  • Strong comparison principle for p-harmonic functions in Carnot-Caratheodory spaces, (with L. Capogna), Proc. Amer. Math. Soc. 146 (2018), no. 10, 4265-4274.

  • Sobolev functions in the critical case are uniformly continuous in s-Ahlfors regular metric spaces when s less than or equal to one, Proc. Amer. Math. Soc. 145 (2017), no. 1, 267-272.

  • Lipschitz continuity and convexity preserving for solutions of semilinear evolution equations in the Heisenberg group, (with Q. Liu and J. J. Manfredi), Calc. Var. Partial Differential Equations 55 (2016), no.4, Art. 80, 25pp.

  • Sobolev embedding on a sphere containing an arbitrary Cantor set in the image, (with P. Hajlasz), Geom. Dedicata. 184 (2016), 159--173.

  • A game-theoretic proof of convexity preserving properties for motion by curvature, (with Q. Liu and A. Schikorra), Indiana Univ. Math. J. 65 (2016), 171--197.