#### Volume 23, issue 1 (2019)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement Author Index To Appear ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Other MSP Journals
Quasi-asymptotically conical Calabi–Yau manifolds

### Appendix: Ronan J Conlon, Frédéric Rochon and Lars Sektnan

Geometry & Topology 23 (2019) 29–100
##### 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 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.

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