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arXiv · 1906.10588

A Liouville type theorem to $2$-Hessian equations

Yan He·Haoyang Sheng·Ni Xiang
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Abstract

In this paper, we proved that any 2-convex solution $u$ of $\sigma_2(D^2u)=1$ 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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Yan He, Haoyang Sheng, Ni Xiang. 2019-06-25. A Liouville type theorem to $2$-Hessian equations. https://arxiv.org/abs/1906.10588

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