# 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.

## Key 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.