Uniqueness of some cylindrical tangent cones to special Lagrangians

We show that if an exact special Lagrangian N subset of C-n has a multiplicity one, cylindrical tangent cone of the form R-k x C where C is a special Lagrangian cone with smooth, connected link, then this tangent cone is unique provided C satisfies an integrability condition. This applies, for example, when C = C-HL(m) is the Harvey-Lawson Tm-1 cone for m&NOTEQUexpressionL;8, 9.

Automated summary

This article studies a condition that an exact special Lagrangian N subset of C-n has a multiplicity one. When C is a special Lagrangian cone with a smooth, connected link and satisfies an integrability condition, the corresponding cylindrical tangent cone is unique. This result applies, for example, when C = C-HL(m) is the Harvey-Lawson Tm-1 cone for m≠8, 9.