2015/12/10 by Yohsuke Imagi, Dominic Joyce, Joana Oliveira dos Santos +1 · 1 citation
Mathematics · #Geometric and Algebraic Topology #Geometry and complex manifolds #Geometric Analysis and Curvature Flows
paper · doi:10.1215/00127094-3167275
We prove two main results. (1) Suppose that L is a closed, embedded, exact special Lagrangian m-fold in Cm asymptotic at infinity to the union Π1∪Π2 of two transverse special Lagrangian planes Π1,Π2 in Cm for m≥3. Then L is one of the explicit Lawlor neck family of examples found by Lawlor. (2) Suppose that L is a closed, embedded, exact Lagrangian mean curvature flow expander in Cm asymptotic at infinity to the union Π1∪Π2 of two transverse Lagrangian planes Π1,Π2 in Cm for m≥3. Then L is one of the explicit family of examples in recent work by Joyce, Lee, and Tsui. If instead L is immersed rather than embedded, the only extra possibility in (1), (2) is L=Π1∪Π2. Our methods, which are new and can probably be used to prove other similar uniqueness theorems, involve J-holomorphic curves, Lagrangian Floer cohomology, and Fukaya categories from symplectic topology.