Steady gradient K\"ahler-Ricci solitons on crepant resolutions of Calabi-Yau cones

Abstract

We show that, up to the flow of the soliton vector field, there exists a unique complete steady gradient K\"ahler-Ricci soliton in every K\"ahler class of an equivariant crepant resolution of a Calabi-Yau cone converging at a polynomial rate to Cao's steady gradient K\"ahler-Ricci soliton on the cone.

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