| Abstract: |
| This presentation introduces some progress in the interior regularity theory of fully nonlinear equations. For the equation of positive scalar curvature (also known as the 2-Hessian equation), we completely resolve the interior second-order derivative estimates in the three-dimensional case and for convex solutions. In higher dimensions, for the special Lagrangian curvature equation, we establish a priori interior curvature estimates in both the critical phase case and the convex case. |
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