# Prescribed mean curvature equation on the unit ball in the presence of reflection or rotation symmetry

## TL;DR

This paper proves the existence of conformal metrics with prescribed mean curvature on the unit ball, under certain symmetry conditions, using the flow method.

## Contribution

It introduces new existence results for the prescribed mean curvature problem on the unit ball with symmetry constraints, employing the flow method.

## Key findings

- Existence of conformal metrics with prescribed mean curvature under symmetry conditions
- Application of flow method to solve the prescribed curvature problem
- Extension of previous results to symmetric cases

## Abstract

Using the flow method, we prove some existence results for the problem of prescribing the mean curvature on the unit ball. More precisely, we prove that there exists a conformal metric on the unit ball such that its mean curvature is $f$, when $f$ possesses certain reflection or rotation symmetry.