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
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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 -