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A Liouville type theorem to $2$-Hessian equations (1906.10588v1)
Published 25 Jun 2019 in math.AP
Abstract: In this paper, we proved that any 2-convex solution $u$ of $\sigma_2(D2u)=1$ with a quadratic growth must be a quadratic polynomial in $\mathbb{R}n\ (n\geq 3 )$ by using a Pogorelov estimate and the global gradient estimate. And we give a positive answer to the unresolved issue in \cite{CX}.
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