Subgraphs with large minimum $\ell$-degree in hypergraphs where almost   all $\ell$-degrees are large
  Let $G$ be an $r$-uniform hypergraph on $n$ vertices such that all but at most $\varepsilon \binom{n}{\ell}$ $\ell$-subsets of vertices have degree at least $p \binom{n-\ell}{r-\ell}$.   We show that $G$ contains a large subgraph with high minimum $\ell$-degree. 
Victor Falgas-Ravry and Allan Lo
math.CO