Asymptotic analysis for surfaces with large constant mean curvature and free boundaries

TL;DR

This paper proves that simply connected constant mean curvature surfaces with free boundaries in a domain tend to concentrate at points where the boundary's mean curvature is critical, under bounded area conditions.

Contribution

It establishes a link between the concentration points of H-surfaces and critical points of the boundary's mean curvature, providing new insights into their asymptotic behavior.

Findings

Surfaces concentrate at critical points of boundary mean curvature.

Concentration occurs under bounded area conditions.

Results apply to simply connected H-surfaces with free boundaries.

Abstract

We prove that simply connected H-surfaces with bounded area and free boundary in a domain necessarily concentrate at a critical point of the mean curvature of the boundary of this domain.