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Global weak solutions of the Teichmüller harmonic map flow into general targets

Abstract:
We analyse finite-time singularities of the Teichm¨uller harmonic map flow – a natural gradient flow of the harmonic map energy – and find a canonical way of flowing beyond them in order to construct global solutions in full generality. Moreover, we prove a noloss-of-topology result at finite time, which completes the proof that this flow decomposes an arbitrary map into a collection of branched minimal immersions connected by curves.
Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's Version

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Publisher copy:
10.2140/apde.2019.12.815

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Trinity College
ORCID:
0000-0002-9139-1400
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Publisher:
Mathematical Sciences Publishers Publisher's website
Journal:
Analysis and PDE Journal website
Volume:
12
Issue:
3
Pages:
815–842
Publication date:
2018-10-25
Acceptance date:
2018-06-29
DOI:
EISSN:
1948-206X
ISSN:
2157-5045
Pubs id:
pubs:864193
URN:
uri:ff1505ee-a6e3-4a18-bb31-5ee5a3d48186
UUID:
uuid:ff1505ee-a6e3-4a18-bb31-5ee5a3d48186
Local pid:
pubs:864193

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