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Type: Journal article
Title: Higher order Seiberg–Witten functionals and their associated gradient flows
Author: Saratchandran, H.
Citation: Manuscripta Mathematica, 2019; 160(3-4):411-481
Publisher: Springer Nature
Issue Date: 2019
ISSN: 0025-2611
Statement of
Hemanth Saratchandran
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.
Rights: © Springer-Verlag GmbH Germany, part of Springer Nature 2018
DOI: 10.1007/s00229-018-1092-2
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Mathematical Sciences publications

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