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arXiv · 2609.07458

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 $W^{2,1}$ semi-convex viscosity solution to the three-dimensional subcritical special Lagrangian equation is area-minimizing and smooth. Furthermore, we prove the smoothness of $W^{2,1}\cap C^{1,1/3+}$ semi-convex viscosity solutions. This yields progress on the conjecture proposed by Wang--Yuan [WY13]. The corresponding results in higher dimensions are also established.

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Zhenyu Fan. 2026-09-07. Geometric regularity for semi-convex viscosity solutions to the special Lagrangian equation. https://arxiv.org/abs/2609.07458

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