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 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) |
---|---|
Pages (from-to) | 3201-3214 |
Number of pages | 14 |
Journal | Duke Mathematical Journal |
Volume | 171 |
Issue number | 15 |
DOIs | |
State | Published - Oct 15 2022 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- General Mathematics