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
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We show that convex solutions of the special Lagrangian equation are smooth, answering a 2009 question of Chen-Warren-Yuan.听 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.听 For general semiconvex solutions of the sigma-2 equation, we show that entire smooth solutions are quadratic, confirming the 2010 guess of Chang-Yuan.听
Based on joint works with Arunima Bhattacharya, Jingyi Chen, and Yu Yuan.