A criterion on instability of rotating cylindrical surfaces

TL;DR

This paper establishes a criterion for the instability of rotating cylindrical surfaces, identifying a critical length beyond which the surface becomes unstable, extending classical results by Plateau and Rayleigh.

Contribution

It introduces a new instability criterion for rotating cylindrical surfaces, generalizing classical stability results for constant mean curvature columns.

Findings

A specific length $l_0$ is identified as a threshold for instability.

Surfaces longer than $l_0$ are proven to be unstable.

The results extend classical stability criteria to rotating surfaces.

Abstract

We consider a column of a rotating stationary surface in Euclidean space. We obtain a value $l_0>0$ in such way that if the length $l$ of column satisfies $l>l_0$, then the surface is instable. This extends, in some sense, previous results due to Plateau and Rayleigh for columns of surfaces with constant mean curvature.