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https://hdl.handle.net/2440/137205
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Type: | Journal article |
Title: | A New Higher Order Yang-Mills-Higgs Flow on Riemannian 4-Manifolds |
Author: | Saratchandran, H. Zhang, J. Zhang, P. |
Citation: | Bulletin of the Australian Mathematical Society, 2022; 107(2):320-329 |
Publisher: | Cambridge University Press |
Issue Date: | 2022 |
ISSN: | 0004-9727 1755-1633 |
Statement of Responsibility: | Hemanth Saratchandran, Jiaogen Zhang and Pan Zhang |
Abstract: | Let (M, g) be a closed Riemannian 4-manifold and let E be a vector bundle over M with structure group G, where G is a compact Lie group. We consider a new higher order Yang–Mills–Higgs functional, in which the Higgs field is a section of Ω0(adE). We show that, under suitable conditions, solutions to the gradient flow do not hit any finite time singularities. In the case that E is a line bundle, we are able to use a different blow-up procedure and obtain an improvement of the long-time result of Zhang [‘Gradient flows of higher order Yang–Mills–Higgs functionals’, J. Aust. Math. Soc. 113 (2022), 257–287]. The proof relies on properties of the Green function, which is very different from the previous techniques. |
Keywords: | higher order Yang–Mills–Higgs flow; line bundle; long-time existence |
Description: | Published online first 29 November 2023 |
Rights: | © 2022 Cambridge University Press |
DOI: | 10.1017/S0004972722001265 |
Grant ID: | http://purl.org/au-research/grants/arc/12201001 |
Published version: | http://dx.doi.org/10.1017/s0004972722001265 |
Appears in Collections: | Australian Institute for Machine Learning publications |
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