A New Higher Order Yang-Mills-Higgs Flow on Riemannian 4-Manifolds

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dc.contributor.authorSaratchandran, H.
dc.contributor.authorZhang, J.
dc.contributor.authorZhang, P.
dc.date.issued2022
dc.descriptionPublished online first 29 November 2023
dc.description.abstractLet (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.
dc.description.statementofresponsibilityHemanth Saratchandran, Jiaogen Zhang and Pan Zhang
dc.identifier.citationBulletin of the Australian Mathematical Society, 2022; 107(2):320-329
dc.identifier.doi10.1017/S0004972722001265
dc.identifier.issn0004-9727
dc.identifier.issn1755-1633
dc.identifier.urihttps://hdl.handle.net/2440/137205
dc.language.isoen
dc.publisherCambridge University Press
dc.relation.granthttp://purl.org/au-research/grants/arc/12201001
dc.rights© 2022 Cambridge University Press
dc.source.urihttps://doi.org/10.1017/s0004972722001265
dc.subjecthigher order Yang–Mills–Higgs flow; line bundle; long-time existence
dc.titleA New Higher Order Yang-Mills-Higgs Flow on Riemannian 4-Manifolds
dc.typeJournal article
pubs.publication-statusPublished

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