Mathematical Research Letters

Volume 30 (2023)

Number 1

Blowing up extremal Poincaré type manifolds

Pages: 185 – 238

DOI: https://dx.doi.org/10.4310/MRL.2023.v30.n1.a9

Author

Lars Martin Sektnan (Département de mathématiques, Université du Québec à Montréal, Québec, Canada; and Department of Mathematical Sciences, University of Gothenburg, Sweden)

Abstract

We prove a version of the Arezzo–Pacard–Singer blow-up theorem in the setting of Poincaré type metrics. We apply this to give new examples of extremal Poincaré type metrics. A key feature is an additional obstruction which has no analogue in the compact case. This condition is conjecturally related to ensuring the metrics remain of Poincaré type.

Full Text (PDF format)

Received 7 April 2020

Received revised 4 February 2021

Accepted 18 November 2022

Published 21 June 2023