Blow-up models for forced mean curvature flow

Determine whether bb-translating solitons with nonzero forcing parameter bb occur as blow-up models of the forced mean curvature flow with constant forcing.

Background

A bb-translating soliton is an eternal translating solution of mean curvature flow with a constant forcing term, satisfying H = c<T,bd> + bb. The paper distinguishes the case bb = 0, where translating solitons are established models of Type II singularities of ordinary mean curvature flow, from the case bb 7 0, where the geometric role of such solitons as singularity models for the corresponding forced flow remains unresolved.

Resolving this question would clarify whether nonzero-forcing translating solitons arise naturally as blow-up limits of forced mean curvature flow, extending the known Type II singularity interpretation from ordinary translating solitons to the bb-dependent setting.