  We present the results of first-principle numerical simulations of Euclidean
SU(3) Yang-Mills plasma rotating with a high imaginary angular frequency. The
rigid Euclidean rotation is introduced via ``rotwisted'' boundary conditions
along imaginary time direction. The Polyakov loop in the co-rotating Euclidean
reference frame shows the emergence of a spatially inhomogeneous
confining-deconfining phase through a broad crossover transition. A
continuation of our numerical results to Minkowski spacetime suggests that the
gluon plasma, rotating at real angular frequencies, produces a new
inhomogeneous phase possessing the confining phase near the rotation axis and
the deconfinement phase in the outer regions. The inhomogeneous phase structure
has a purely kinematic origin, rooted in the Tolman-Ehrenfest effect in a
rotating medium. We also derive the Euclidean version of the Tolman-Ehrenfest
law in imaginary time formalism and discuss two definitions of temperature at
imaginary Euclidean rotation.
