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We establish a vanishing result for the $L_{q,p}$-cohomology ($q\ge p$) of a twisted cylinder, which is a generalization of a warped cylinder. The result is new even for warped cylinders. We base on the methods for proving the $(p,q)$ Sobolev--Poincare inequality developed by L.~Shartser.

The Sobolev–Poincaré inequality and the $L_{q,p}$-cohomology of twisted cylinders