Min-max theory, Willmore conjecture and the energy of links

Fernando C. Marques; André Neves

doi:10.1007/s00574-013-0030-x

Min-max theory, Willmore conjecture and the energy of links

Fernando C. Marques, André Neves

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this paper we give an overview of some aspects of the min-max theory of minimal surfaces, and discuss recent applications to conformally invariant problems in Geometry and Topology. The goal is to explain what the proofs of the Willmore conjecture for surfaces and the Freedman-He-Wang conjecture for links share in common. This is based on joint work of the authors [19] and on joint work of I. Agol and the authors [1].

Original language	English (US)
Pages (from-to)	681-707
Number of pages	27
Journal	Bulletin of the Brazilian Mathematical Society
Volume	44
Issue number	4
DOIs	https://doi.org/10.1007/s00574-013-0030-x
State	Published - Dec 2013
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Willmore
conformal geometry
links in space
min-max method
minimal surfaces

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10.1007/s00574-013-0030-x

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title = "Min-max theory, Willmore conjecture and the energy of links",

abstract = "In this paper we give an overview of some aspects of the min-max theory of minimal surfaces, and discuss recent applications to conformally invariant problems in Geometry and Topology. The goal is to explain what the proofs of the Willmore conjecture for surfaces and the Freedman-He-Wang conjecture for links share in common. This is based on joint work of the authors [19] and on joint work of I. Agol and the authors [1].",

keywords = "Willmore, conformal geometry, links in space, min-max method, minimal surfaces",

author = "Marques, {Fernando C.} and Andr{\'e} Neves",

note = "Funding Information: Received 10 June 2013. *Corresponding author. The first author was partly supported by CNPq-Brazil and FAPERJ. The second author was partly supported by Marie Curie IRG Grant and ERC Start Grant.",

year = "2013",

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doi = "10.1007/s00574-013-0030-x",

language = "English (US)",

volume = "44",

pages = "681--707",

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TY - JOUR

T1 - Min-max theory, Willmore conjecture and the energy of links

AU - Marques, Fernando C.

AU - Neves, André

N1 - Funding Information: Received 10 June 2013. *Corresponding author. The first author was partly supported by CNPq-Brazil and FAPERJ. The second author was partly supported by Marie Curie IRG Grant and ERC Start Grant.

PY - 2013/12

Y1 - 2013/12

N2 - In this paper we give an overview of some aspects of the min-max theory of minimal surfaces, and discuss recent applications to conformally invariant problems in Geometry and Topology. The goal is to explain what the proofs of the Willmore conjecture for surfaces and the Freedman-He-Wang conjecture for links share in common. This is based on joint work of the authors [19] and on joint work of I. Agol and the authors [1].

AB - In this paper we give an overview of some aspects of the min-max theory of minimal surfaces, and discuss recent applications to conformally invariant problems in Geometry and Topology. The goal is to explain what the proofs of the Willmore conjecture for surfaces and the Freedman-He-Wang conjecture for links share in common. This is based on joint work of the authors [19] and on joint work of I. Agol and the authors [1].

KW - Willmore

KW - conformal geometry

KW - links in space

KW - min-max method

KW - minimal surfaces

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VL - 44

SP - 681

EP - 707

JO - Bulletin of the Brazilian Mathematical Society

JF - Bulletin of the Brazilian Mathematical Society

IS - 4

ER -

Min-max theory, Willmore conjecture and the energy of links

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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