Vol. 302, No. 2, 2019

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Yamabe equation on some complete noncompact manifolds

Guodong Wei

Vol. 302 (2019), No. 2, 717–739
Abstract

We consider the Yamabe equation on a complete noncompact Riemannian manifold and find some geometric conditions on the manifold such that the Yamabe problem admits a bounded positive solution.

Keywords
Yamabe problem, noncompact manifold, Yamabe constant, blow-up analysis, pointed Cheeger–Gromov topology
Mathematical Subject Classification 2010
Primary: 53C21
Secondary: 35B40, 35J61, 35R01
Milestones
Received: 2 August 2017
Revised: 5 January 2019
Accepted: 4 April 2019
Published: 27 November 2019
Authors
Guodong Wei
Key Laboratory of Pure and Applied Mathematics
School of Mathematical Sciences
Peking University
Beijing
China