QiRui LI
Postdoctoral Fellow
Room 3.69, Hanna Neumann Building #145
Mathematical Sciences Institute
Australian National University
Canberra, ACT 2601, Australia
Phone: (612) 6125 1020
qirui
dot li
at anu
dot edu
dot au
Research Interests
My area of research is nonlinear elliptic and parabolic partial differential equations and their applications. I am interested in MongeAmp\`ere equations, kHessian equations, MongeKantorovich transportation problem, convex geometric analysis, geometric flows, and curvature problems in Riemannian manifolds.
Papers

The $L_p$ dual Minkowski problem and related parabolic flows.
(with H. Chen). Preprint.
[pdf]

The $L_p$BrunnMinkowski inequality for $p<1$
(with S. Chen, Y. Huang and J. Liu). Preprint.
[pdf]

Variations of a class of MongeAmp\`ere type functionals and their applications
(with H. Chen and S. Chen). Submitted.
[pdf]

Asymptotic convergence for a class of fully nonlinear curvature flows
(with W. Sheng and X.J. Wang). Submitted.
[pdf]

Flow by Gauss curvature to the Aleksandrov and dual Minkowski problems
(with W. Sheng and X.J. Wang).
Accepted by J. Eur. Math. Soc. in 2017.
[pdf]

Infinitely many solutions for centroaffine Minkowski problem.
To appear in Int. Math. Res. Not.
https://doi.org/10.1093/imrn/rnx284.
[pdf]

Continuity for the Monge mass transfer problem in two dimensions
(with F. Santambrogio and X.J. Wang).
Arch. Rational Mech. Anal. 231 (2019), no. 2, 10451071.
[pdf]

The logarithmic Minkowski problem for nonsymmetric measures
(with S. Chen and G. Zhu).
Trans. Amer. Math. Soc. 371 (2019), no. 4, 26232641.
[pdf]

On the planar dual Minkowski problem
(with S. Chen). Adv. Math. 333 (2018), 87117.
[pdf]

A class of optimal transportation problems on the sphere,
Dedicated to Professor G.C. Dong on the occasion of his 90th birthday
(with X.J. Wang).
Sci Sin Math. 48 (2018), no. 1, 181200.
[pdf]

Two dimensional MongeAmp\`ere equations under incomplete H\"older assumptions.
Math. Res. Lett. 24 (2017), no. 2, 485506.
[pdf]

On the $L_p$ MongeAmpère equation (with S. Chen and G. Zhu).
J. Differential Equations 263 (2017), no. 8, 4997–5011.
[pdf]

Multiple solutions of the $L_p$Minkowski problem
(with Y. He and X.J. Wang).
Calc. Var. Partial Differential Equations
55 (2016), no. 5, Paper No. 117, 13 pp.
[pdf]

Regularity of the homogeneous MongeAmp\`ere equation (with X.J. Wang).
Discrete Contin. Dyn. Syst. 35 (2015), no. 12, 60696084.
[pdf]

Regularity in Monge's mass transfer problem
(with F. Santambrogio and X.J. Wang).
J. Math. Pures Appl. (9) 102 (2014), no. 6, 10151040.
[pdf]

Positivity of MaTrudingerWang curvature on Riemannian surfaces
(with S.Z. Du).
Calc. Var. Partial Differential Equations 51 (2014), no. 34, 495523.
[pdf]

Closed hypersurfaces with prescribed Weingarten curvature in Riemannian manifolds
(with W. Sheng).
Calc. Var. Partial Differential Equations 48 (2013), no. 12, 4166.
[pdf]

Some Dirichlet problems arising from conformal geometry (with W. Sheng).
Pacific J. Math. 251 (2011), no. 2, 337359.
[pdf]

Surfaces expanding by the power of the Gauss curvature flow.
Proc. Amer. Math. Soc. 138 (2010), no. 11, 40894102.
[pdf]