BaoZhi Chu

collaborators

4 papers

math.AP2026

On Singular Sets of Fully Nonlinear Uniformly Elliptic Equations

BaoZhi Chu

For continuous viscosity solutions $u$ of fully nonlinear uniformly elliptic equations $F (D^{2} u) = 0$ , the work of Nadirashvili--Tkachev--Vlăduţ shows that $u$ need not be $C^{2}$ in d…

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…

math.AP2024

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…