Abstract
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 by-product of the work on special Lagrangian equations. Warren’s rare saddle entire solution in 2014 confirmed the necessity of the semiconvexity assumption.
Citation
Ravi Shankar. Yu Yuan. "Rigidity for general semiconvex entire solutions to the sigma-2 equation." Duke Math. J. 171 (15) 3201 - 3214, 15 October 2022. https://doi.org/10.1215/00127094-2022-0034
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