We study the boundary behaviors of a complete conformal metric which solves the \(\sigma _k\)-Ricci problem on the interior of a manifold with boundary. We establish asymptotic expansions and also \(C^1\) and \(C^2\) estimates for this metric multiplied by the square of the distance in a small neighborhood of the boundary.

中文翻译：

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具有负 Ricci 曲率的完全共形度量的边界扩展

我们研究了一个完整的保形度量的边界行为，它解决了带有边界的流形内部的\(\sigma _k\) -Ricci 问题。我们建立了渐近扩展以及\(C^1\)和\(C^2\)估计，该度量乘以边界的一个小邻域中的距离的平方。