A reflection principle for minimal surfaces in smooth three manifolds

TL;DR

This paper establishes a reflection principle for minimal surfaces within smooth three-dimensional manifolds, broadening the understanding of their symmetry properties without requiring the ambient space to be analytic.

Contribution

It introduces a reflection principle applicable to minimal surfaces in smooth, non-analytic three-manifolds, providing explicit applications in purely smooth ambient spaces.

Findings

Reflection principle proven for minimal surfaces in smooth manifolds

Applicable to non-analytic ambient spaces

Explicit example provided in smooth manifold setting

Abstract

We prove a reflection principle for minimal surfaces in smooth (non necessarily analytic) three manifolds and we give an explicit application when the ambient space is just a smooth manifold.