# Research

I primarily work in the field of convex geometric analysis. I am particularly interested in the Minkowski-type problems for geometric measures obtained by “differentiating” geometric invariants. These problems generate Monge-Ampère equations on the unit sphere and can be tackled from a PDE point of view (e.g., geometric flow).

I am also interested in isoperimetric inequalities (both affine and non-affine, geometric and functional).

This page contains a list of peer-reviewed papers and preprints. It is updated periodically. You can also find my articles on __my Google Scholar profile__, or on __MathSciNet__ (subscription required).

## Publications

- (with D. Xi) General affine invariances related to Mahler volume.
*submitted.* - (with K. Böröczky, E. Lutwak, D. Yang, and G. Zhang) The Gauss image problem.
*Communications on Pure and Applied Mathematics*, in press. - (with K. Böröczky, E. Lutwak, D. Yang, and G. Zhang) The dual Minkowski problem for symmetric convex bodies.
*Adv. Math.*356: 106805, 2019. - (with C. Chen and Y. Huang) Smooth solutions to the $L_p$ dual Minkowski problem.
*Math. Ann.*373 (3-4):953-976, 2019. - The $L_p$ Aleksandrov problem for origin-symmetric polytopes.
*Proc. Amer. Math. Soc.*147 (10):4477-4492, 2019. - (with Y. Huang) On the $L_p$ dual Minkowski problem.
*Adv. Math.*332: 57-84, 2018. - Existence of solutions to the even dual Minkowski problem.
*J. Differential Geom.*110 (3): 543–572, 2018. - The dual Minkowski problem for negative indices.
*Calc. Var. Partial Differential Equations*56:18,2017. arXiv - On $L_p$-affine surface area and curvature measures.
*Int. Math. Res. Not. IMRN*(5): 1387-1423, 2016. arXiv