#### 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 ${\sigma }_{2}$ 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
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