The Cauchy problem for gradient generalized Ricci solitons on a bundle gerbe

TL;DR

This paper establishes the well-posedness of the Cauchy problem for gradient generalized Ricci solitons on bundle gerbes, providing new insights into their self-similar solutions and initial data equations.

Contribution

It introduces a novel characterization of self-similar solutions of the generalized Ricci flow via automorphisms of abelian bundle gerbes.

Findings

Proves well-posedness of the analytic Cauchy problem for these solitons.

Solves initial data equations on every compact Riemann surface.

Provides a new characterization of self-similar solutions using automorphisms.

Abstract

We prove well-posedness of the analytic Cauchy problem for gradient generalized Ricci solitons on an abelian bundle gerbe and solve the initial data equations on every compact Riemann surface. Along the way, we provide a novel characterization of the self-similar solutions of the generalized Ricci flow by means of families of automorphisms of the underlying abelian bundle gerbe covering families of diffeomorphisms isotopic to the identity.