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arXiv · 2208.02736

Uniqueness of some cylindrical tangent cones to special Lagrangians

Tristan C. Collins·Yang Li
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Abstract

We show that if an exact special Lagrangian $N\subset \mathbb{C}^n$ has a multiplicity one, cylindrical tangent cone of the form $\mathbb{R}^{k}\times \mathbf{C}$ where $\mathbf{C}$ is a special Lagrangian cone with smooth, connected link, then this tangent cone is unique provided $\mathbf{C}$ satisfies an integrability condition. This applies, for example, when $\mathbf{C}= \mathbf{C}_{HL}^{m}$ is the Harvey-Lawson $T^{m-1}$ cone for $m\ne 8,9$.

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Tristan C. Collins, Yang Li. 2022-08-04. Uniqueness of some cylindrical tangent cones to special Lagrangians. https://arxiv.org/abs/2208.02736

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