The Willmore Conjecture

Fernando C. Marques; André Neves

doi:10.1365/s13291-014-0104-8

The Willmore Conjecture

Fernando C. Marques, André Neves

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

18 Scopus citations

Abstract

The Willmore conjecture, proposed in 1965, concerns the quest to find the best torus of all. This problem has inspired a lot of mathematics over the years, helping bringing together ideas from subjects like conformal geometry, partial differential equations, algebraic geometry and geometric measure theory. In this article we survey the history of the conjecture and our recent solution through the min-max approach. We finish with a discussion of some of the many open questions that remain in the field.

Original language	English (US)
Pages (from-to)	201-222
Number of pages	22
Journal	Jahresbericht der Deutschen Mathematiker-Vereinigung
Volume	116
Issue number	4
DOIs	https://doi.org/10.1365/s13291-014-0104-8
State	Published - Dec 2014
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)

Keywords

Bending energy
Min-max theory
Minimal surfaces
Willmore surfaces

Access to Document

10.1365/s13291-014-0104-8

Cite this

@article{4f50a518df174e71bf916c96c9abbccc,

title = "The Willmore Conjecture",

abstract = "The Willmore conjecture, proposed in 1965, concerns the quest to find the best torus of all. This problem has inspired a lot of mathematics over the years, helping bringing together ideas from subjects like conformal geometry, partial differential equations, algebraic geometry and geometric measure theory. In this article we survey the history of the conjecture and our recent solution through the min-max approach. We finish with a discussion of some of the many open questions that remain in the field.",

keywords = "Bending energy, Min-max theory, Minimal surfaces, Willmore surfaces",

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

note = "Funding Information: 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. Publisher Copyright: {\textcopyright} 2014, Deutsche Mathematiker-Vereinigung and Springer-Verlag Berlin Heidelberg.",

year = "2014",

month = dec,

doi = "10.1365/s13291-014-0104-8",

language = "English (US)",

volume = "116",

pages = "201--222",

journal = "Jahresbericht der Deutschen Mathematiker-Vereinigung",

publisher = "Springer Science and Business Media Deutschland GmbH",

number = "4",

}

TY - JOUR

T1 - The Willmore Conjecture

AU - Marques, Fernando C.

AU - Neves, André

N1 - Funding Information: 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. Publisher Copyright: © 2014, Deutsche Mathematiker-Vereinigung and Springer-Verlag Berlin Heidelberg.

PY - 2014/12

Y1 - 2014/12

N2 - The Willmore conjecture, proposed in 1965, concerns the quest to find the best torus of all. This problem has inspired a lot of mathematics over the years, helping bringing together ideas from subjects like conformal geometry, partial differential equations, algebraic geometry and geometric measure theory. In this article we survey the history of the conjecture and our recent solution through the min-max approach. We finish with a discussion of some of the many open questions that remain in the field.

AB - The Willmore conjecture, proposed in 1965, concerns the quest to find the best torus of all. This problem has inspired a lot of mathematics over the years, helping bringing together ideas from subjects like conformal geometry, partial differential equations, algebraic geometry and geometric measure theory. In this article we survey the history of the conjecture and our recent solution through the min-max approach. We finish with a discussion of some of the many open questions that remain in the field.

KW - Bending energy

KW - Min-max theory

KW - Minimal surfaces

KW - Willmore surfaces

UR - http://www.scopus.com/inward/record.url?scp=84983243153&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84983243153&partnerID=8YFLogxK

U2 - 10.1365/s13291-014-0104-8

DO - 10.1365/s13291-014-0104-8

M3 - Article

AN - SCOPUS:84983243153

VL - 116

SP - 201

EP - 222

JO - Jahresbericht der Deutschen Mathematiker-Vereinigung

JF - Jahresbericht der Deutschen Mathematiker-Vereinigung

IS - 4

ER -

The Willmore Conjecture

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this