Quasi-asymptotically conical Calabi-Yau manifolds

Abstract

We construct new examples of quasi-asymptotically conical (QAC) Calabi-Yau manifolds that are not quasi-asymptotically locally Euclidean (QALE). We do so by first providing a natural compactification of QAC-spaces by manifolds with fibred corners and by giving a definition of QAC-metrics in terms of an associated Lie algebra of smooth vector fields on this compactification. Thanks to this compactification and the Fredholm theory for elliptic operators on QAC-spaces developed by the second author and Mazzeo, we can in many instances obtain Kähler QAC-metrics having Ricci potential decaying sufficiently fast at infinity. This allows us to obtain QAC Calabi-Yau metrics in the Kähler classes of these metrics by solving a corresponding complex Monge-Ampère equation.

42 pages, 5 figures, final version

References in corpus (1)

• Fredholm theory for elliptic operators on quasi-asymptotically conical spaces

Cited by in corpus (4)

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• Low energy limit for the resolvent of some fibered boundary operators
• Injectivity radius of manifolds with a Lie structure at infinity