TL;DR
This paper explores the geometric evolution of the moduli space of a single abelian Higgs vortex as the vortex size varies, revealing similarities to Ricci flow through theoretical and special case analyses.
Contribution
It introduces a novel perspective by linking the vortex moduli space metric evolution to Ricci flow, supported by calculations and theoretical arguments.
Findings
The vortex moduli space metric evolves similarly to Ricci flow.
The Bradlow parameter controls the vortex size and influences the geometry.
Special case calculations support the Ricci flow analogy.
Abstract
The metric on the moduli space of one abelian Higgs vortex on a surface has a natural geometrical evolution as the Bradlow parameter, which determines the vortex size, varies. It is shown by various arguments, and by calculations in special cases, that this geometrical flow has many similarities to Ricci flow.
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