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We construct an expanding gradient Ricci soliton in dimension three over thetopological manifold R x T^2 (the product of a line and a torus) that aproachesasymptotically a constant curvature cusp at one end, and a flat manifold on theother end. We prove that this is the only gradient soliton with this topology,provided the curvature is negatively pinched, -1/4 < sec < 0, at the time-zeromanifold (normalizing the soliton to be born at time -1).

An asymptotically cusped three dimensional expanding gradient Ricci soliton