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Flowing maps to minimal surfaces

Abstract:

We introduce a flow of maps from a compact surface of arbitrary genus to an arbitrary Riemannian manifold which has elements in common with both the harmonic map flow and the mean curvature flow, but is more effective at finding minimal surfaces. In the genus 0 case, our flow is just the harmonic map flow, and it tries to find branched minimal 2-spheres as in Sacks-Uhlenbeck (1981) and Struwe (1985), etc. In the genus 1 case, we show that our flow is exactly equivalent to that considered by D...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted manuscript

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Publisher copy:
10.1353/ajm.2016.0035

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Trinity College
ORCID:
0000-0002-9139-1400
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Publisher:
Johns Hopkins University Press Publisher's website
Journal:
American Journal of Mathematics Journal website
Volume:
138
Issue:
4
Pages:
1095-1115
Publication date:
2016-08-05
DOI:
EISSN:
1080-6377
ISSN:
0002-9327
Pubs id:
pubs:581597
URN:
uri:6c04db10-3601-4f96-b3c2-1ddad9e06086
UUID:
uuid:6c04db10-3601-4f96-b3c2-1ddad9e06086
Local pid:
pubs:581597

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