Steady gradient Kähler-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 Kähler-Ricci soliton in every Kähler class of an equivariant crepant resolution of a Calabi-Yau cone converging at a polynomial rate to Cao's steady gradient Kähler-Ricci soliton on the cone.

arXiv comment92 pages

References in corpus (5)

• Asymptotically conical Calabi-Yau manifolds, I
• Classification results for expanding and shrinking gradient Kähler-Ricci solitons
• On rotationally symmetric Kahler-Ricci solitons
• Complete Calabi-Yau metrics from P^2 # 9 \bar P^2
• Steady Kähler-Ricci solitons on crepant resolutions of finite quotients of ${\mathbb{C}}^n$

Cited by in corpus (1)

• On the Gluing Construction of Translating Solitons to Lagrangian Mean Curvature Flow