Asymptotic stability of local Helfrich minimizers

TL;DR

This paper proves that local minimizers of the Canham-Helfrich energy are asymptotically stable in a fluid vesicle dynamics model, using a Lojasiewicz-Simon inequality, extending previous work.

Contribution

It establishes the asymptotic stability of local Helfrich minimizers within a relaxational fluid vesicle model, providing a rigorous mathematical proof.

Findings

Local minimizers are asymptotically stable under the model.

The proof employs a Lojasiewicz-Simon inequality.

Supports the understanding of vesicle shape stability.

Abstract

We show that local minimizers of the Canham-Helfrich energy are asymptotically stable with respect to a model for relaxational fluid vesicle dynamics that we already studied in previous papers ([12, 11]). The proof is based on a Lojasiewicz-Simon inequality.