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