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Nonlinear Analysis

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

Speaker: Yu Yuan, University of Washington

Location:  zoom
Date & time: Wednesday, 15 December 2021 at 9:30AM - 10:30AM

Abstract: We present a rigidity result for general semiconvex entire solutions to the sigma-2 equation. Two decades ago, this result was obtained in three dimensions, as a byproduct of the work on special Lagrangian equations. A decade ago in a joint work with Chang, this result was shown for almost convex entire solutions. Warren's rare saddle entire solution confirms the necessity of the semiconvexity assumption. Recall the classical Liouville rigidity for the Laplace equation or the sigma-1 equation and Jörgens-Calabi-Pogorelov rigidity for the Monge-Ampère equation or the sigma-n equation: all convex entire solutions to those equations in general n dimensions must be quadratic. This is joint work with Ravi Shankar.

The Zoom link for this seminar will always be:
https://rutgers.zoom.us/j/96430905091?pwd=Tkp4N0FlRnk3ZXZLWTl6LzRHdkNZdz09
Meeting ID: 964 3090 5091 Passcode: 491508

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