Rigidity for general semiconvex entire solutions to the sigma-2 equation

TL;DR

This paper proves that all semiconvex entire solutions to the sigma-2 equation are quadratic polynomials, extending previous results that were limited to almost convex solutions.

Contribution

It generalizes prior work by establishing the quadratic polynomial nature for all semiconvex solutions, not just almost convex ones.

Findings

Semiconvex solutions are quadratic polynomials.

Extension of previous convexity-based results.

Broader class of solutions characterized as quadratic.

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.