Smoothing out positively curved metric cones by Ricci expanders

TL;DR

This paper explores the desingularization of positively curved metric cones using Ricci expanders, demonstrating the connectedness of the moduli space of such geometric structures.

Contribution

It introduces a method to smooth positively curved metric cones with Ricci expanders and proves the moduli space of these structures is connected.

Findings

Connectedness of the moduli space of conical positively curved gradient Ricci expanders.

Establishment of deformation techniques for positively curved geometric structures.

Abstract

We investigate the possibility of desingularizing a positively curved metric cone by an expanding gradient Ricci soliton with positive curvature operator. This amounts to study the deformation of such geometric structures. As a consequence, we prove that the moduli space of conical positively curved gradient Ricci expanders is connected.