Regularity of asymptotically conical Ricci-flat Kähler metrics

Details Regularity of asymptotically conical Ricci-flat Kähler metrics Regularity of asymptotically conical Ricci-flat Kähler metrics

2009-12-19

arxiv.org/abs/0912.3946v5

Mathematics

Differential Geometry

28 pages.

Scientific paper

Using methods of A. Grigor'yan and L. Saloff-Coste we prove that on a manifold with a conical end the heat kernel has a Gaussian bound. This result is applied to asymptotically conical K\"ahler manifolds. It is a result of the author and R. Goto that a crepant resolution of a Ricci-flat K\"ahler cone admits a Ricci-flat K\"ahler metric asymptotic to the cone metric in every K\"ahler class. We prove the sharp rate of convergence of the metric to the cone metric. For compact K\"ahler classes this is the same as for the Ricci-flat ALE metrics of P. Kronheimer and D. Joyce.

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