Min-max theory and the energy of links
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- by Ian Agol, Fernando C. Marques and André Neves
- J. Amer. Math. Soc. 29 (2016), 561-578
- DOI: https://doi.org/10.1090/jams/835
- Published electronically: June 4, 2015
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Abstract:
Freedman, He, and Wang conjectured in 1994 that the Möbius energy should be minimized, among the class of all nontrivial links in Euclidean space, by the stereographic projection of the standard Hopf link. We prove this conjecture using the min-max theory of minimal surfaces.References
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Bibliographic Information
- Ian Agol
- Affiliation: Department of Mathematics, University of California, 970 Evans Hall #3840, Berkeley, California 94720-3840
- MR Author ID: 671767
- ORCID: 0000-0002-4254-8483
- Email: ianagol@math.berkeley.edu
- Fernando C. Marques
- Affiliation: Department of Mathematics, Princeton University, Fine Hall, Princeton, New Jersey 08544
- MR Author ID: 689130
- Email: coda@impa.br
- André Neves
- Affiliation: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2RH, United Kingdom
- MR Author ID: 733597
- Email: a.neves@imperial.ac.uk
- Received by editor(s): September 19, 2012
- Received by editor(s) in revised form: April 10, 2015
- Published electronically: June 4, 2015
- Additional Notes: The first author was supported by DMS-0806027 and DMS-1105738.
The second author was partly supported by CNPq-Brazil, FAPERJ, and Math-Amsud.
The third author was partly supported by Marie Curie IRG Grant, ERC Start Grant, and Leverhulme Award. - © Copyright 2015 American Mathematical Society
- Journal: J. Amer. Math. Soc. 29 (2016), 561-578
- MSC (2010): Primary 57M25; Secondary 53C42, 49Q20
- DOI: https://doi.org/10.1090/jams/835
- MathSciNet review: 3454383