Special Lagrangians with multiple isolated singularities
arXiv:2607.26302
The paper extends a perturbation technique to construct special Lagrangian submanifolds in \(\mathbb{C}^m\) that have multiple prescribed isolated conical singularities, using a bridge principle for regular special Lagrangian cones.
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 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 with multiple prescribed isolated conical singularities.
34 pages. Comments are welcome!