RIGIDITY FOR GENERAL SEMICONVEX ENTIRE SOLUTIONS TO THE SIGMA-2 EQUATION

Ravi Shankar, Yu Yuan

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 languageEnglish (US)
Pages (from-to)3201-3214
Number of pages14
JournalDuke Mathematical Journal
Volume171
Issue number15
DOIs
StatePublished - Oct 15 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics

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