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math.AP2024
Quadratic Hessian equation
Yu Yuan
We survey quadratic Hessian equations: definition, background, rigidity of entire solutions, regularity of viscosity solutions, a priori Hessian estimates, and open problems.
math.AP2024
A constant rank theorem for special Lagrangian equations
W. Jacob Ogden, Yu Yuan
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 fo…