Global Existence for the Seiberg-Witten Flow

2009/09/10 by Min-Chun Hong, Hong, Min-Chun, Lorenz Schabrun +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.0909.1855

arxiv created 2010/08/19 · arxiv updated 2015/03/13

Abstract

We introduce the gradient flow of the Seiberg-Witten functional on a compact, orientable Riemannian 4-manifold and show the global existence of a unique smooth solution to the flow. The flow converges uniquely in C^∞ up to gauge to a critical point of the Seiberg-Witten functional.

Related

• Seiberg-Witten Flow in Higher Dimensions
• Higher order Seiberg-Witten functionals and their associated gradient flows
• Einstein Metrics, Four-Manifolds, and Differential Topology
• Solutions to the Seiberg-Witten equations in all dimensions
• Variational Aspects of the Seiberg-Witten Functional