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Quasi-asymptotically
conical Calabi–Yau manifolds
Ronan J Conlon, Anda Degeratu and Frédéric RochonAppendix: Ronan J Conlon, Frédéric Rochon and Lars Sektnan |
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Geometry & Topology 23 (2019) 29–100
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Abstract |
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We construct new examples of quasi-asymptotically conical () Calabi–Yau manifolds that are not quasi-asymptotically locally Euclidean (). We do so by first providing a natural compactification of –spaces by manifolds with fibered corners and by giving a definition of –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 –spaces developed by the second author and Mazzeo, we can in many instances obtain Kähler –metrics having Ricci potential decaying sufficiently fast at infinity. This allows us to obtain Calabi–Yau metrics in the Kähler classes of these metrics by solving a corresponding complex Monge–Ampère equation. |
Keywords
Calabi–Yau metrics, quasi-asymptotically conical metrics,
manifolds with corners
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Mathematical Subject Classification 2010
Primary: 53C55, 58J05
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References |
Publication
Received: 21 March 2017
Revised: 12 February 2018
Accepted: 14 June 2018
Published: 5 March 2019
Proposed: Simon Donaldson
Seconded: Tobias H Colding, Gang Tian
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Authors |
| Ronan J Conlon | |
| Department of Mathematics and
Statistics Florida International University Miami, FL United States |
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| Anda Degeratu | |
| Fachbereich Mathematik Universität Stuttgart Stuttgart Germany |
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| Frédéric Rochon | |
| Département de Mathématiques Université du Québec à Montréal Montréal, QC Canada |
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| Ronan J Conlon | |
| Frédéric Rochon | |
| Lars Sektnan | |
| Département de Mathématiques Université du Québec à Montréal Montréal, QC Canada |
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