A note on perfect matchings in uniform hypergraphs

We determine the \emph{exact} minimum $\mathrm{\ell }$-degree threshold for perfect matchings in $k$-uniform hypergraphs when the corresponding threshold for perfect fractional matchings is significantly less than $\frac{1}{2} \binom{n}{k- \ell}$. This extends our previous results that determine the minimum $\mathrm{\ell }$-degree thresholds for perfect matchings in $k$-uniform hypergraphs for all $\mathrm{\ell }\ge k\mathrm{/}2$ and provides two new (exact) thresholds: $(k,\mathrm{\ell })=(5,2)$ and $(7,3)$.