A complete gradient Ricci soliton with nonnegative Ricci curvature and a convex potential satisfying weighted integral conditions must be Ricci flat and split a line; concave bounded-Ricci potentials force a non-shrinking soliton with at most one critical point of scalar curvature.
S., Three-manifolds with positive Ricci curvature , J
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On Ricci solitons whose potential is convex
A complete gradient Ricci soliton with nonnegative Ricci curvature and a convex potential satisfying weighted integral conditions must be Ricci flat and split a line; concave bounded-Ricci potentials force a non-shrinking soliton with at most one critical point of scalar curvature.