Abstract
We study the stability of unduloids with free boundary in the domain B between two parallel hyperplanes in Rn+1. If the unduloid has one half of period in B and is sufficiently close to a cylinder, then for 2 ≤ n ≤ 10, it is unstable; while for n ≥ 11, it is stable. If the unduloid has two or more halves of period in B and is sufficiently close to a cylinder, then for all n ≥ 2, it is unstable.
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