Liouville property and existence of entire solutions of Hessian equations

Cong Wang; Jiguang Bao

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arXiv · 2203.02646

Liouville property and existence of entire solutions of Hessian equations

Cong Wang·Jiguang Bao

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Abstract

In this paper, we establish the existence and uniqueness theorem for entire solutions of Hessian equations with prescribed asymptotic behavior at infinity. This extends the previous results on Monge-Amp\`{e}re equations. Our approach also makes the prescribed asymptotic order optimal within the range preset in exterior Dirichlet problems. In addition, we show a Liouville type result for $k$-convex solutions. This partly removes the $(k+1)$- or $n$-convexity restriction imposed in existing work.

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Cong Wang, Jiguang Bao. 2022-03-05. Liouville property and existence of entire solutions of Hessian equations. https://arxiv.org/abs/2203.02646

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