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Quasi-asymptotically conical Calabi–Yau manifolds

Ronan J Conlon, Anda Degeratu and Frédéric Rochon

Appendix: Ronan J Conlon, Frédéric Rochon and Lars Sektnan

Geometry & Topology 23 (2019) 29–100

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 fibered 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.

Calabi–Yau metrics, quasi-asymptotically conical metrics, manifolds with corners
Mathematical Subject Classification 2010
Primary: 53C55, 58J05
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
Ronan J Conlon
Department of Mathematics and Statistics
Florida International University
Miami, FL
United States
Anda Degeratu
Fachbereich Mathematik
Universität Stuttgart
Frédéric Rochon
Département de Mathématiques
Université du Québec à Montréal
Montréal, QC
Ronan J Conlon
Frédéric Rochon
Lars Sektnan
Département de Mathématiques
Université du Québec à Montréal
Montréal, QC