Abstract
We prove two main results. (1) Suppose that is a closed, embedded, exact special Lagrangian -fold in asymptotic at infinity to the union of two transverse special Lagrangian planes in for . Then is one of the explicit Lawlor neck family of examples found by Lawlor. (2) Suppose that is a closed, embedded, exact Lagrangian mean curvature flow expander in asymptotic at infinity to the union of two transverse Lagrangian planes in for . Then is one of the explicit family of examples in recent work by Joyce, Lee, and Tsui. If instead is immersed rather than embedded, the only extra possibility in (1), (2) is . Our methods, which are new and can probably be used to prove other similar uniqueness theorems, involve -holomorphic curves, Lagrangian Floer cohomology, and Fukaya categories from symplectic topology.
Citation
Yohsuke Imagi. Dominic Joyce. Joana Oliveira dos Santos. "Uniqueness results for special Lagrangians and Lagrangian mean curvature flow expanders in ." Duke Math. J. 165 (5) 847 - 933, 1 April 2016. https://doi.org/10.1215/00127094-3167275
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