Loose Hamilton cycles in hypergraphs

We prove that any kk-uniform hypergraph on nn vertices with minimum degree at least n2(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 kk-uniform case, our argument here is considerably simplified by applying the recent hypergraph blow-up lemma of Keevash.