Regularity and rigidity for special Lagrangian and sigma-2 equations

Regularity and rigidity for special Lagrangian and sigma-2 equations

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Ravi Shankar, Princeton University
Fine Hall 314

Hybrid Event

Zoom linkhttps://princeton.zoom.us/j/594605776

We show that convex solutions of the special Lagrangian equation are smooth, answering a 2009 question of Chen-Warren-Yuan.  A similar technique yields an optimal classification of regularity for Lagrangian mean curvature type equations, and regularity for almost convex solutions of the sigma-2 equation.  For general semiconvex solutions of the sigma-2 equation, we show that entire smooth solutions are quadratic, confirming the 2010 guess of Chang-Yuan. 

Based on joint works with Arunima Bhattacharya, Jingyi Chen, and Yu Yuan.