Abstract: We continue the discussion on LMCF in Hyperkahler 4-manifolds with circle symmetry. In this talk, we will discuss the hyperkahler moment map reduction of the LMCF where special Lagrangians will be mapped to certain line segments in the image and the LMCF will be reduced to a modified curve shortening flow. With all these understanding, we will give a heuristic outline of the Thomas conjecture and Thomas-Yau conjecture in this setting. Reference: Lotay, J.D. and Oliveira, G., 2020. Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz. arXiv preprint arXiv:2002.10391. Lotay, J.D. and Oliveira, G., 2023. Neck pinch singularities and Joyce conjectures in Lagrangian mean curvature flow with circle symmetry. arXiv preprint arXiv:2305.05744.