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<p>Constant rank theorems are obtained for saddle solutions to the special Lagrangian equation and the quadratic Hessian equation. The argument also leads to Liouville type results for the special Lagrangian equation with subcritical phase, matching the known rigidity results for semiconvex entire solutions to the quadratic Hessian equation.</p>

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A constant rank theorem for special Lagrangian Equations

  • 期刊论文

  • 发表日期：

    2025年9月9日

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  • W. Jacob Ogden,
  • Yu YUAN

摘要

Constant rank theorems are obtained for saddle solutions to the special Lagrangian equation and the quadratic Hessian equation. The argument also leads to Liouville type results for the special Lagrangian equation with subcritical phase, matching the known rigidity results for semiconvex entire solutions to the quadratic Hessian equation.