论文标题
liouville财产和整个Hessian方程解决方案的存在
Liouville property and existence of entire solutions of Hessian equations
论文作者
论文摘要
在本文中，我们为无限远的渐近行为的整个Hessian方程解决方案的整个解决方案的存在和唯一定理建立了。这扩展了Monge-Ampère方程的先前结果。我们的方法还使规定的渐近顺序在外部Dirichlet问题的范围内最佳。此外，我们还显示了$ K $ -CONVEX解决方案的Liouville类型结果。这部分删除了在现有工作中施加的$（k+1）$ - 或$ n $ convexity限制。
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-Ampère 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.
