Vol. 311, No. 1, 2021

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The $\sigma_{2}$ Yamabe problem on conic spheres, II: Boundary compactness of the moduli

Hao Fang and Wei Wei

Vol. 311 (2021), No. 1, 33–51
DOI: 10.2140/pjm.2021.311.33
Abstract

We prove a convergence theorem on the moduli space of constant σ2 metrics for conic 4-spheres. We show that when a numerical condition is convergent to the boundary case, the geometry of conic 4-spheres converges to the boundary case while preserving capacity.

Keywords
$\sigma_2$ Yamabe, conic metric, boundary compactness
Mathematical Subject Classification 2010
Primary: 53C25
Milestones
Received: 24 September 2019
Revised: 29 July 2020
Accepted: 18 November 2020
Published: 17 March 2021
Authors
Hao Fang
Department of Mathematics
University of Iowa
Iowa City, IA 52242
United States
Wei Wei
Shanghai Center for Mathematical Sciences
Fudan University
Shanghai 200438
China