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

TL;DR

This paper proves a convergence theorem for the moduli space of constant  metrics on conic 4-spheres, showing boundary behavior and capacity preservation as parameters approach boundary cases.

Contribution

It establishes a boundary compactness result for the moduli space of  metrics on conic 4-spheres, advancing understanding of geometric limits.

Findings

Convergence of the moduli space under boundary conditions

Boundary case limits preserve geometric capacity

Provides a framework for boundary compactness in conic sphere metrics

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.