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Singular metrics with negative scalar curvature
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Cheng, Man-Chuen, Lee, Man-Chun and Tam, Luen-Fai (2022) Singular metrics with negative scalar curvature. International Journal of Mathematics, 33 (7). 2250047. doi:10.1142/s0129167x22500471 ISSN 1793-6519.
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Official URL: https://doi.org/10.1142/s0129167x22500471
Abstract
Motivated by the work of Li and Mantoulidis [C. Li, C. Mantoulidis, Positive scalar curvature with skeleton singularities, Math. Ann. 374(1–2) (2019) 99–131], we study singular metrics which are uniformly Euclidean [Formula: see text] on a compact manifold [Formula: see text] ([Formula: see text]) with negative Yamabe invariant [Formula: see text]. It is well known that if [Formula: see text] is a smooth metric on [Formula: see text] with unit volume and with scalar curvature [Formula: see text], then [Formula: see text] is Einstein. We show, in all dimensions, the same is true for metrics with edge singularities with cone angles [Formula: see text] along codimension-2 submanifolds. We also show in three dimensions, if the Yamabe invariant of connected sum of two copies of [Formula: see text] attains its minimum, then the same is true for [Formula: see text] metrics with isolated point singularities.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
SWORD Depositor: | Library Publications Router | ||||||||
Journal or Publication Title: | International Journal of Mathematics | ||||||||
Publisher: | World Scientific Pub Co Pte Ltd | ||||||||
ISSN: | 1793-6519 | ||||||||
Official Date: | June 2022 | ||||||||
Dates: |
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Volume: | 33 | ||||||||
Number: | 7 | ||||||||
Article Number: | 2250047 | ||||||||
DOI: | 10.1142/s0129167x22500471 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access |
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