6 papers · 1 filter
A Liouville theorem for convex functions with periodic Monge-Ampère measure
Tianling Jin, YanYan Li, Hung V. Tran +1
We study global convex solutions of the Monge-Ampère equation \[ \det D^2 u = μ\quad \text{in } \mathbb{R}^n, \] where is a nonnegative locally finite periodic B…
Composite media, almost touching disks and the maximum principle
YanYan Li, Ben Weinkove
We consider the setting of two disks in a domain in which are almost touching and have finite and positive conductivities, giving rise to a divergence form elliptic…
Conformal metrics of constant scalar curvature with unbounded volumes
Liuwei Gong, Yanyan Li
For , we construct a smooth metric on the standard -dimensional sphere such that there exists a sequence of smooth metrics $\{\tilde{g}_k\}_…
Liouville Theorem with Boundary Conditions from Chern--Gauss--Bonnet Formula
BaoZhi Chu, YanYan Li, Zongyuan Li
The curvature and the boundary curvature arise naturally from the Chern--Gauss--Bonnet formula for manifolds with boundary. In this paper, we prove a…
On the fully nonlinear Yamabe problem with constant boundary mean curvature. I
BaoZhi Chu, YanYan Li, Zongyuan Li
In a recent paper, we established optimal Liouville-type theorems for conformally invariant second-order elliptic equations in the Euclidean space. In this work, we prove an optima…
Liouville theorems for conformally invariant fully nonlinear equations. I
BaoZhi Chu, YanYan Li, Zongyuan Li
A fundamental theorem of Liouville asserts that positive entire harmonic functions in Euclidean spaces must be constant. A remarkable Liouville-type theorem of Caffarelli-Gidas-Spr…