Smooth compactness of elasticae

TL;DR

This paper establishes a smooth compactness theorem for elasticae, excluding straight segments, and applies it to demonstrate stability of minimizers under fixed boundary conditions.

Contribution

It introduces a new smooth compactness theorem for elasticae and derives stability results for minimizers with clamped boundary data.

Findings

Proved a smooth compactness theorem for elasticae.

Established stability of minimizers with fixed boundary conditions.

Excluded straight segments from the compactness result.

Abstract

We prove a smooth compactness theorem for the space of elasticae, unless the limit curve is a straight segment. As an application, we obtain smooth stability results for minimizers with respect to clamped boundary data.