On p-Willmore Disks with Boundary Energies

TL;DR

This paper investigates a combined boundary and interior energy functional for surface immersions, focusing on equilibrium shapes of topological disks and p-Willmore energies, inspired by physical models of elastic rods.

Contribution

It introduces a new energy model incorporating boundary and curvature-dependent interior terms, analyzing equilibrium configurations for disks and p-Willmore energies.

Findings

Characterization of equilibrium configurations for the proposed energy.

Analysis of p-Willmore disks with boundary energies.

Insights into the stability of elastic surface models.

Abstract

We consider an energy functional on surface immersions which includes contributions from both boundary and interior. Inspired by physical examples, the boundary is modeled as the center line of a generalized Kirchhoff elastic rod, while the interior term is arbitrarily dependent on the mean curvature and linearly dependent on the Gaussian curvature. We study equilibrium configurations for this energy in general among topological disks, as well as specifically for the class of examples known as p-Willmore energies.