Let k and n be two integers, with $k\ge 3$, $n\equiv 0(\mathrm{mod}k)$, and n sufficiently large. We determine the $(k-1)$-degree threshold for the existence of a rainbow perfect matchings in n-vertex k-uniform hypergraph. This implies the result of Rödl, Ruciński, and Szemerédi on the $(k-1)$-degree threshold for the existence of perfect matchings in n-vertex k-uniform hypergraphs. In our proof, we identify the extremal configurations of closeness, and consider whether or not the hypergraph is close to the extremal configuration. In addition, we also develop a novel absorbing device and generalize the absorbing lemma of Rödl, Ruciński, and Szemerédi.

令k和n为两个整数，其中$k\ge 3$,$n==0（\mathrm{模组}k）$，并且n足够大。我们确定$（k-1）$-n -顶点k -均匀超图中存在彩虹完美匹配的度阈值。这意味着 Rödl、Ruciński 和 Szemerédi 在$（k-1）$- n -顶点k -均匀超图中存在完美匹配的度阈值。在我们的证明中，我们识别了接近度的极值配置，并考虑超图是否接近极值配置。此外，我们还开发了一种新颖的吸收装置并推广了 Rödl、Ruciński 和 Szemerédi 的吸收引理。