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https://hdl.handle.net/2440/126823
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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 1432-1785 |
Statement of Responsibility: | 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 |
Appears in Collections: | Aurora harvest 8 Mathematical Sciences publications |
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