Stability of Cylinders in E(κ, τ ) Homogeneous Spaces

Abstract

We extend the classical Plateau–Rayleigh instability criterion in the E(κ, τ ) spaces.We prove the existence of a positive number L0 > 0 such that if a truncated circular cylinder of radius ρ in E(κ, τ) has length L > L0, then it is unstable. This number L0 depends on κ, τ and ρ. The value L0 is sharp under axially symmetric variations of the surface. We also extend this result for the partitioning problem in E(κ, τ ).