Boundary value problems for Willmore curves in $\mathbb{R}^2$

TL;DR

This paper addresses boundary value problems for Willmore curves in the plane, providing solutions to classical boundary conditions and advancing understanding of their geometric properties.

Contribution

It introduces solutions to the Navier and Dirichlet boundary value problems for Willmore curves in two-dimensional space.

Findings

Explicit solutions to Navier and Dirichlet problems for Willmore curves.

Enhanced understanding of boundary conditions for Willmore curves.

Potential applications in geometric analysis and shape optimization.

Abstract

In this paper the Navier problem and the Dirichlet problem for Willmore curves in $\mathbb{R}^2$ is solved.