Special Weingarten surfaces with planar convex boundary

TL;DR

This paper proves that certain special Weingarten surfaces with convex planar boundaries are topological disks, extending classical results to a broader class of surfaces.

Contribution

It establishes a Ros-Rosenberg type theorem for Special Weingarten surfaces with convex planar boundaries, showing they are topological disks under mild conditions.

Findings

Such surfaces are topological disks

The theorem extends classical results to Special Weingarten surfaces

Conditions for the disk topology are mild and general

Abstract

We prove a Ros-Rosenberg theorem in the setting of Special Weingarten surfaces. We show that a compact, connected, embedded, Special Weingarten surface in $\mathhb{R}^3$ with planar convex boundary is a topological disk under mild suitable assumptions.