A gap theorem for translating solitons to Lagrangian mean curvature flow

In this paper, we prove a gap theorem for translating solitons to the almost calibrated Lagrangian mean curvature flow. More precisely, we prove that there exists a constant λ>0λ>0 such that if |H|2⩽λ|T|2|H|2⩽λ|T|2, then the translating soliton must be a plane. We also obtain a similar result for symplectic mean curvature flow.