= Solution
With <planar anchoring> on the cylindrical side wall, \b[uniform axial alignment $\mathbf n=\hat{\mathbf z}$ is a simple defect-free profile]. The axial direction is tangent at every wall point, so it satisfies the lateral boundary everywhere without elastic distortion.
This assumes degenerate <planar anchoring>, or an azimuthal preference compatible with axial alignment. End constraints, selected circumferential anchoring or imposed twist can favor another state. <planar anchoring> alone does not require a circumferential vortex. The original axial-section sketch shows the uniform axial option.
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