Zhi-Hui Zhang

Exterior Serrin Rigidity for the Homogeneous{k}-Hessian Equation

In this paper, we study the exterior overdetermined problems for the homogeneous k-Hessian equations $$\sigma_k(D^2u)=0\quad\text{in}~\mathbb{R}^n\setminus\overline{\Omega}$$ in three dimensional regimes. For $2\le k<n$ and smooth strictly star-shaped domain $\Omega\Subset\R^n$, we establish ball rigidity results in al...