A Liouville type theorem to $2$-Hessian equations

Yan He; Haoyang Sheng; Ni Xiang

A Liouville type theorem to $2$-Hessian equations

Analysis of PDEs 2019-06-26 v1

Authors: Yan He , Haoyang Sheng , Ni Xiang

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}.

Keywords

liouville theorem painlevé equations

Cite

@article{arxiv.1906.10588,
  title  = {A Liouville type theorem to $2$-Hessian equations},
  author = {Yan He and Haoyang Sheng and Ni Xiang},
  journal= {arXiv preprint arXiv:1906.10588},
  year   = {2019}
}

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