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PreprintCC BY 4.0arXiv

Special Lagrangians with multiple isolated singularities

  • Bryan Dimler
  • Filippo Gaia
Open at sourcePDFDOICite

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 ℂm 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. When applied to the graphical special Lagrangian cone in ℂ5 recently discovered by Bhattacharya, Orriols, and Skorobogatova, we obtain infinite families of C1,1 viscosity solutions to the special Lagrangian equation having any finite number of isolated singularities.

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Cite

BibTeXRIS
BibTeX
@misc{dimler2026special,
  title = {{Special Lagrangians with multiple isolated singularities}},
  author = {Bryan Dimler and Filippo Gaia},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.26302},
  eprint = {2607.26302},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.26302},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Special Lagrangians with multiple isolated singularities
AU  - Bryan Dimler
AU  - Filippo Gaia
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2607.26302
UR  - https://arxiv.org/abs/2607.26302
AB  - 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 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. When applied to the graphical special Lagrangian cone in ℂ^5 recently discovered by Bhattacharya, Orriols, and Skorobogatova, we obtain infinite families of C^1,1 viscosity solutions to the special Lagrangian equation having any finite number of isolated singularities.
ER  -