We show that every general semiconvex entire solution to the sigma-2 equation is a quadratic polynomial. A decade ago, this result was shown for almost convex solutions. Two decades ago, this result was obtained in three dimensions, as a byproduct of the work on special Lagrangian equations. Warren's rare saddle entire solution in 2014 confirmed the necessity of the semiconvexity assumption.
|Original language||English (US)|
|Number of pages||14|
|Journal||Duke Mathematical Journal|
|State||Published - Oct 15 2022|
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