Higher order Seiberg-Witten functionals and their associated gradient flows

2018/02/22 by Hemanth Saratchandran, Saratchandran, Hemanth
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1802.08573

arxiv created 2018/02/22 · arxiv updated 2018/02/26

Abstract

We define functionals generalising the Seiberg-Witten functional on closed spin^c manifolds, involving higher order derivatives of the curvature form and spinor field. We then consider their associated gradient flows and, using a gauge fixing technique, are able to prove short time existence for the flows. We then prove energy estimates along the flow, and establish local L²-derivative estimates. These are then used to show long time existence of the flow in sub-critical dimensions. In the critical dimension, we are able to show that long time existence is obstructed by an L^k+2 curvature concentration phenomenon.

Related

• Global Existence for the Seiberg-Witten Flow
• Seiberg-Witten Flow in Higher Dimensions
• Gradient Flows of Higher Order Yang-Mills-Higgs Functionals
• Higher order Yang-Mills flow
• Solutions to the Seiberg-Witten equations in all dimensions