Variational properties of the total inverse mean curvature in the plane under boundary constraints

TL;DR

This paper investigates the variational properties of the total inverse mean curvature for curves in the half-plane with fixed boundary, identifying critical points, their stability, and minimality properties.

Contribution

It characterizes the existence and stability of critical points of the total inverse mean curvature under boundary constraints in the half-plane.

Findings

Critical points exist with prescribed area.

Such critical points are strongly stable.

Critical points exhibit local minimality.

Abstract

We study the variational behavior of the total inverse mean curvature of curves with prescribed boundary in the half-plane. We characterize the existence of critical points with prescribed area. We show that such critical points are strongly stable. As an application, we prove a local minimality property.