Symmetry Results for classical solutions of Monge-Ampere system in the plane

TL;DR

This paper proves that classical solutions to a Monge-Ampere system in the plane are symmetric about a point using the moving planes method, linking the results to a differential geometry problem.

Contribution

It establishes symmetry of solutions for a Monge-Ampere system in the plane, a novel application of the moving planes method in this context.

Findings

Solutions are symmetric about some point in the plane.

The symmetry result applies to systems arising from differential geometry.

Method demonstrates the effectiveness of moving planes for Monge-Ampere systems.

Abstract

In this paper, by the method of moving planes, we prove the symmetry result which says that classical solutions of Monge-Ampere system in the whole plane are symmetric about some point. Our system under consideration comes from the differential geometry problem.