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

16 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

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10.1365/s13291-014-0104-8

Cite this

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

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

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AU - Neves, André

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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

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The Willmore Conjecture

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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