Ricci Yang-Mills flow on surfaces

2007/10/29 by Jeffrey Streets, Streets, Jeffrey · 1 citation
Mathematics · #53C07 #53C44 #53C80 #58J35 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:53C07 #msc:53C44 #msc:53C80 #msc:58J35

paper · pdf · doi:10.48550/arxiv.0710.5487

openalex publication_date 2007/10/29 · arxiv created 2009/07/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the behaviour of the Ricci Yang-Mills flow for U(1) bundles on surfaces. We show that existence for the flow reduces to a bound on the isoperimetric constant. In the presence of such a bound, we show that on S², if the bundle is nontrivial, the flow exists for all time. For higher genus surfaces the flow always exists for all time. The volume normalized flow always exists for all time and converges to a constant scalar curvature metric with the bundle curvature F parallel. Finally, in an appendix we classify all gradient solitons of this flow on surfaces.

Citations

• A note on uniformization of Riemann surfaces by Ricci flow

Cited by

• Stability of the Ricci Yang-Mills flow at Einstein Yang-Mills metrics

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