Projectability of stable, partially free $H$-surfaces in the non-perpendicular case

TL;DR

This paper proves a new projectability theorem for stable $H$-surfaces with partially free boundaries, allowing non-perpendicular contact with the support surface, extending classical results and including uniqueness and existence corollaries.

Contribution

It generalizes existing theorems on $H$-surfaces by allowing non-perpendicular boundary contact and provides new uniqueness and existence results.

Findings

Established a projectability theorem for non-perpendicular free boundary $H$-surfaces.

Extended classical theorems to more general boundary contact conditions.

Provided corollaries on uniqueness and existence of such surfaces.

Abstract

A projectability result is proved for surfaces of prescribed mean curvature (shortly called $H$-surfaces) spanned in a partially free boundary configuration. Hereby, the $H$-surface is allowed to meet the support surface along its free trace non-perpendicularly. The main result generalizes known theorems due to Hildebrandt-Sauvigny and the author himself and is in the spirit of the well known projectability theorems due to Rad\'o and Kneser. A uniqueness and an existence result are included as corollaries.