Regularity of asymptotically conical Ricci-flat Kähler metrics

Abstract

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 Kähler manifolds. It is a result of the author and R. Goto that a crepant resolution of a Ricci-flat Kähler cone admits a Ricci-flat Kähler metric asymptotic to the cone metric in every Kähler class. We prove the sharp rate of convergence of the metric to the cone metric. For compact Kähler classes this is the same as for the Ricci-flat ALE metrics of P. Kronheimer and D. Joyce.

arXiv comment28 pages.

References in corpus (3)

• Symmetry-breaking vacua and baryon condensates in AdS/CFT
• Sasakian Geometry, Hypersurface Singularities, and Einstein Metrics
• Calabi-Yau structures and Einstein-Sasakian structures on crepant resolutions of isolated singularities

Cited by in corpus (9)

• Asymptotically conical Calabi-Yau manifolds, I
• Baryonic symmetries and M5 branes in the AdS_4/CFT_3 correspondence
• On sharp rates and analytic compactifications of asymptotically conical Kähler metrics
• Complete Calabi-Yau metrics from P^2 # 9 \bar P^2
• Asymptotically conical Calabi-Yau metrics on quasi-projective varieties
• ALE Calabi-Yau metrics with conical singularities along a compact divisor
• Calabi-Yau structures and Einstein-Sasakian structures on crepant resolutions of isolated singularities
• Ricci-flat metrics on the cone over ${\mathbb{CP}}^2\#\overline{{\mathbb{CP}}^2}$
• The AdS/CFT Correspondence and Symmetry Breaking