Zixiao Liu

collaborators

2 papers

math.AP2023

Entire solutions to the parabolic Monge--Ampère equation with unbounded nonlinear growth in time

Ning An, Jiguang Bao, Zixiao Liu

The Liouville type theorem on the parabolic Monge--Ampère equation $- u_{t} det D^{2} u = 1$ states that any entire parabolically convex classical solution must be of form $- t + ∣ x ∣^{2} /2$ up…

math.AP2023

Existence of entire solutions to the Lagrangian mean curvature equations in supercritical phase

Zixiao Liu, Cong Wang, Jiguang Bao

In this paper, we establish the existence and uniqueness theorem of entire solutions to the Lagrangian mean curvature equations with prescribed asymptotic behavior at infinity. The…