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In this note, we consider the derivative nonlinear Schr\"odinger equation onthe circle. In particular, by adapting Wu's recent argument to the periodicsetting, we prove its global well-posedness in $H^1(\mathbb T)$, provided thatthe mass is less than $4\pi$. Moreover, this mass threshold is independent ofspatial periods.

A remark on global well-posedness of the derivative nonlinear Schr\"odinger equation on the circle