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

Mathematical Subject Classification 2010

Primary: 53C25

Milestones

Received: 24 September 2019

Revised: 29 July 2020

Accepted: 18 November 2020

Published: 17 March 2021