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dc.contributor.author
Pigati, Alessandro
dc.contributor.author
Stern, Daniel
dc.date.accessioned
2020-09-28T10:24:20Z
dc.date.available
2020-09-26T19:39:46Z
dc.date.available
2020-09-28T10:24:20Z
dc.date.issued
2020
dc.identifier.issn
0020-9910
dc.identifier.issn
1432-1297
dc.identifier.other
10.1007/s00222-020-01000-6
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/442868
dc.description.abstract
Given a Hermitian line bundle L→ M over a closed, oriented Riemannian manifold M, we study the asymptotic behavior, as ϵ→ 0 , of couples (uϵ, ∇ ϵ) critical for the rescalings Eϵ(u,∇)=∫M(|∇u|2+ϵ2|F∇|2+14ϵ2(1-|u|2)2)of the self-dual Yang–Mills–Higgs energy, where u is a section of L and ∇ is a Hermitian connection on L with curvature F∇. Under the natural assumption lim sup ϵ→Eϵ(uϵ, ∇ ϵ) < ∞, we show that the energy measures converge subsequentially to (the weight measure μ of) a stationary integral (n- 2) -varifold. Also, we show that the (n- 2) -currents dual to the curvature forms converge subsequentially to 2 πΓ , for an integral (n- 2) -cycle Γ with | Γ | ≤ μ. Finally, we provide a variational construction of nontrivial critical points (uϵ, ∇ ϵ) on arbitrary line bundles, satisfying a uniform energy bound. As a byproduct, we obtain a PDE proof, in codimension two, of Almgren’s existence result for (nontrivial) stationary integral (n- 2) -varifolds in an arbitrary closed Riemannian manifold.
en_US
dc.language.iso
en
en_US
dc.publisher
Springer
en_US
dc.title
Minimal submanifolds from the abelian Higgs model
en_US
dc.type
Journal Article
dc.date.published
2020-09-10
ethz.journal.title
Inventiones Mathematicae
ethz.journal.abbreviated
J. Invent. math.
ethz.size
69 p.
en_US
ethz.grant
Geometric Analysis of Scalar and Non Scalar Conformally invariant Variational Problems
en_US
ethz.identifier.wos
ethz.publication.place
Berlin
en_US
ethz.publication.status
published
en_US
ethz.grant.agreementno
172707
ethz.grant.fundername
SNF
ethz.grant.funderDoi
10.13039/501100001711
ethz.grant.program
Projektförderung in Mathematik, Natur- und Ingenieurwissenschaften (Abteilung II)
ethz.date.deposited
2020-09-26T19:39:53Z
ethz.source
WOS
ethz.eth
yes
en_US
ethz.availability
Metadata only
en_US
ethz.rosetta.exportRequired
true
ethz.COinS
ctx_ver=Z39.88-2004&amp;rft_val_fmt=info:ofi/fmt:kev:mtx:journal&amp;rft.atitle=Minimal%20submanifolds%20from%20the%20abelian%20Higgs%20model&amp;rft.jtitle=Inventiones%20Mathematicae&amp;rft.date=2020&amp;rft.issn=0020-9910&amp;1432-1297&amp;rft.au=Pigati,%20Alessandro&amp;Stern,%20Daniel&amp;rft.genre=article&amp;
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