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arXiv · 2607.26302

Special Lagrangians with multiple isolated singularities

Bryan Dimler·Filippo Gaia
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Abstract

We extend the Caffarelli-Hardt-Simon perturbation argument for truncated regular minimal cones to the special Lagrangian setting and prove a bridge principle for regular special Lagrangian cones in the spirit of Nathan Smale. Our bridge principle yields a general existence theorem for conically singular special Lagrangian submanifolds with prescribed regular tangent cones: for any finite list of such cones in $\mathbb{C}^m$ having the same Lagrangian angle and suitably arranged, there exists a connected special Lagrangian submanifold with boundary and isolated conical singularities whose tangent cones at its singularities are precisely the prescribed cones. In particular, we obtain new special Lagrangian submanifolds in $\mathbb{C}^m$ with multiple prescribed isolated conical singularities.

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Bryan Dimler, Filippo Gaia. 2026-07-28. Special Lagrangians with multiple isolated singularities. https://arxiv.org/abs/2607.26302

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