Yanyan Li

activity

20242026

collaborators

5 papers

math.AP2026

A Liouville theorem for convex functions with periodic Monge-AmpÃ¨re measure

Tianling Jin, YanYan Li, Hung V. Tran +1

We study global convex solutions of the Monge-AmpÃ¨re equation \[ \det D^2 u = Î¼\quad \text{in } \mathbb{R}^n, \] where $I^¼ \neq \equiv 0$ is a nonnegative locally finite periodic B…

math.AP2025

Composite media, almost touching disks and the maximum principle

YanYan Li, Ben Weinkove

We consider the setting of two disks in a domain in $R^{2}$ which are almost touching and have finite and positive conductivities, giving rise to a divergence form elliptic…

math.AP2025

Conformal metrics of constant scalar curvature with unbounded volumes

Liuwei Gong, Yanyan Li

For $n \geq 25$ , we construct a smooth metric $g ~$ on the standard $n$ -dimensional sphere $S^{n}$ such that there exists a sequence of smooth metrics $\{\tilde{g}_k\}_…

math.AP2024

Liouville Theorem with Boundary Conditions from Chern--Gauss--Bonnet Formula

BaoZhi Chu, YanYan Li, Zongyuan Li

The $I ¨ _{k} (A_{g})$ curvature and the boundary $B_{g}^{k}$ curvature arise naturally from the Chern--Gauss--Bonnet formula for manifolds with boundary. In this paper, we prove a…

math.AP2024

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…