Abstract This paper studies singularities of mean curvature flows with integral mean curvature bounds H ∈ L ∞ L loc p H L^L^p₋₎₂ for some p ∈ (n, ∞ ] p (n, ]. For such flows, any backward tangent flow is given by the flow of a stationary cone 𝐂. When p = ∞ p= and 𝐂 is a regular cone, we prove that the backward tangent flow is unique. These results hold for general integral Brakke flows of arbitrary codimension in an open subset U ⊆ R N U^N with H ∈ L ∞ L loc p H L^L^p₋₎₂. For smooth, codimension-one mean curvature flows with H ∈ L ∞ L loc ∞ H L^L^₋₎₂, we also show that, at points where a backward tangent flow is given by an area-minimizing Simons cone, there is an accompanying limit flow given by a smooth Hardt–Simon minimal surface.
Maxwell Stolarski (Wed,) studied this question.