Loose Hamilton cycles in hypergraphs

We prove that any k -uniform hypergraph on n vertices with minimum degree at least n 2 ( k − 1 ) + o ( n ) contains a loose Hamilton cycle. The proof strategy is similar to that used by Kühn and Osthus for the 3-uniform case. Though some additional difficulties arise in the k -uniform case, our argument here is considerably simplified by applying the recent hypergraph blow-up lemma of Keevash.