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Geometric regularity for semi-convex viscosity solutions to the special Lagrangian equation

  • Zhenyu Fan
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Abstract

We prove that the gradient graph of any W2,1 semi-convex viscosity solution to the three-dimensional subcritical special Lagrangian equation is area-minimizing and smooth. Furthermore, we prove the smoothness of W2,1∩ C1,1/3+ semi-convex viscosity solutions. This yields progress on the conjecture proposed by Wang--Yuan [WY13]. The corresponding results in higher dimensions are also established.

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Cite

BibTeXRIS
BibTeX
@misc{fan2026geometric,
  title = {{Geometric regularity for semi-convex viscosity solutions to the special Lagrangian equation}},
  author = {Zhenyu Fan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07458},
  eprint = {2609.07458},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07458},
}
RIS
TY  - UNPB
TI  - Geometric regularity for semi-convex viscosity solutions to the special Lagrangian equation
AU  - Zhenyu Fan
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07458
UR  - https://arxiv.org/abs/2609.07458
AB  - We prove that the gradient graph of any W^2,1 semi-convex viscosity solution to the three-dimensional subcritical special Lagrangian equation is area-minimizing and smooth. Furthermore, we prove the smoothness of W^2,1∩ C^1,1/3+ semi-convex viscosity solutions. This yields progress on the conjecture proposed by Wang--Yuan [WY13]. The corresponding results in higher dimensions are also established.
ER  -