A constant rank theorem for special Lagrangian equations
W. Jacob Ogden, Yu Yuan
TL;DR
This paper establishes constant rank theorems for saddle solutions to special Lagrangian and quadratic Hessian equations, leading to Liouville type results and rigidity conclusions for solutions with specific phase conditions.
Contribution
It introduces new constant rank theorems for special Lagrangian and quadratic Hessian equations, extending rigidity results and Liouville theorems in this context.
Findings
Constant rank theorems for saddle solutions
Liouville type results for subcritical phase
Rigidity results for semiconvex solutions
Abstract
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.
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Taxonomy
TopicsMatrix Theory and Algorithms · Algebraic and Geometric Analysis