Mathematical Research Letters

Volume 30 (2023)

Number 1

Blowing up extremal Poincaré type manifolds

Pages: 185 – 238



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


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.

Received 7 April 2020

Received revised 4 February 2021

Accepted 18 November 2022

Published 21 June 2023