  We show that near-horizon geometries in the presence of a positive
cosmological constant cannot exist with ring topology. In particular, de Sitter
black rings with vanishing surface gravity do not exist. Our result relies on a
known mathematical theorem which is a straightforward consequence of a type of
energy condition for a modified Ricci tensor, similar to the
curvature-dimension conditions for the $m$-Bakry-\'Emery-Ricci tensor.
