  In this work, we construct distance like functions with integral hessian
bound on manifolds with small curvature concentration and use it to construct
Ricci flows on manifolds with possibly unbounded curvature. As an application,
we study the geometric structure of those manifolds without bounded curvature
assumption. In particular, we show that manifolds with Ricci lower bound,
non-negative scalar curvature, bounded entropy, Ahlfors $n$-regular and small
curvature concentration are topologically Euclidean.
