Gravitational instantons with faster than quadratic curvature decay (II)

Abstract

This is our second paper in a series to study gravitational instantons, i.e. complete hyperkäler 4-manifolds with faster than quadratic curvature decay. We prove two main theorems: 1.The asymptotic rate of gravitational instantons to the standard models can be improved automatically. 2.Any ALF-D_k gravitational instanton must be the Cherkis-Hitchin-Ivanov-Kapustin-Lindström-Roček metric.

arXiv commentWe add a corollary and the applications, correct the asymptotic rate of the multi-Taub-NUT metric

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Cited by in corpus (19)

• Nilpotent structures and collapsing Ricci-flat metrics on K3 surfaces
• Gravitational instantons with faster than quadratic curvature decay (III)
• On toric Hermitian ALF gravitational instantons
• Instantons on multi-Taub-NUT Spaces I: Asymptotic Form and Index Theorem
• PL density invariant for type II degenerating K3 surfaces, Moduli compactification and hyperKahler metrics
• Collapsing Ricci-flat metrics on elliptic K3 surfaces
• Asymptotic Geometry of the Moduli Space of Parabolic $SL(2,\mathbb{C})$-Higgs Bundles
• On the geometry of asymptotically flat manifolds
• Perspectives on the Asymptotic Geometry of the Hitchin Moduli Space
• Polystable log Calabi-Yau varieties and Gravitational instantons
• Gravitational instantons with quadratic volume growth
• Collapsing geometry of hyperkähler 4-manifolds and applications
• Umbral Moonshine and String Duality
• Elliptic analysis on collapsing gravitational instantons modelled using the Gibbons-Hawking ansatz
• Hodge theory on ALG${}^{\ast }$ manifolds
• G${}_2$ manifolds with nodal singularities along circles
• Global uniqueness of the minimal sphere in the Atiyah-Hitchin manifold
• The Torelli Theorem for $AL{H}^{\ast }$ Gravitational Instantons
• Asymptotically Calabi metrics and weak Fano manifolds