國立清華大學 數學系

Abstract:

Lagrangian mean curvature flow (LMCF) is a canonical way to deform Lagrangian submanifolds in Calabi--Yau manifolds, with the goal of finding 'special Lagrangians', which are volume-minimizers within their homology classes. Despite its significance, the general long-time behavior of LMCF remains open. In this talk, l will present recent joint work with Chung-Jun Tsai and Albert Wood where we construct a long-time solution to LMCF with an infinite-time singularity, precisely modeled on shrinking Lawlor necks at a specific rate. Our approach utilizes a parabolic gluing construction, inspired by Brendle and Kapouleas' work on ancient Ricci flow.