Abstract: The improved paint roller is configured for use in applying paint. The improved paint roller is configured for use in applying paint to a non-Euclidean application surface wherein the non-Euclidean application surface is selected from the group consisting of a concave surface or a convex surface. The improved paint roller comprises a roller sleeve and a handle. The roller sleeve presents a non-Euclidean face selected from the group consisting of a concave face or a convex face. The roller sleeve is configured for use in applying the paint to the non-Euclidean application surface. Specifically: 1) a roller sleeve presenting a concave face is intended to apply paint upon a convex non-Euclidean application surface; while, 2) the roller sleeve presenting a convex face is intended to apply paint upon a concave non-Euclidean application surface.