Classical Schwarz Reflection Principle for Jenkins-Serrin Type Minimal Surfaces

TL;DR

This paper proves a classical Schwarz reflection principle for Jenkins-Serrin type minimal surfaces in certain homogeneous three-manifolds, extending previous work on reflection principles in Riemannian manifolds.

Contribution

It provides a new proof of the Schwarz reflection principle specifically for Jenkins-Serrin type minimal surfaces in $E(, au)$ spaces, distinct from prior Riemannian manifold results.

Findings

Established the reflection principle for minimal surfaces in $E(, au)$ spaces.

Extended the reflection principle to Jenkins-Serrin type minimal surfaces.

Differentiated techniques from previous Riemannian manifold reflection results.

Abstract

We give a proof of the classical Schwarz reflection principle for Jenkins-Serrin type minimal surfaces in the homogeneous three manifolds $E(\kappa, \tau)$ for $\kappa \leqslant 0$ and $\tau \geqslant 0$. In our previous paper we proved a reflection principle in Riemannian manifolds. The statements and techniques in the two papers are distinct.