Mini-workshop: The Willmore functional and the Willmore conjecture. Abstracts from the mini-workshop held July 21--27, 2013.
type: Item
instance of: scholarly article
title: Mini-workshop: The Willmore functional and the Willmore conjecture. Abstracts from the mini-workshop held July 21--27, 2013.
zbMATH Open document ID: 1349.00217
DOI: 10.4171/OWR/2013/37
published in: Oberwolfach Reports
publication date: 2016-11-30T00:00:00Z
review text: Summary: The Willmore functional evaluated on a surface immersed into Euclidean space is given by the \(L^2\)-norm of its mean curvature. The interest for studying this functional comes from various directions. First, it arises in applications from biology and physics, where it is used to model surface tension in the Helfrich model for bilipid layers, or in General Relativity where it appears in Hawking's quasi-local mass. Second, the mathematical properties justify consideration of the Willmore functional in its own right. The Willmore functional is one of the most natural extrinsic curvature functionals for immersions. Its critical points solve a fourth order Euler-Lagrange equation, which has all minimal surfaces as solutions.
Mathematics Subject Classification ID: 00B05
Mathematics Subject Classification ID: 00B25
Mathematics Subject Classification ID: 53-06
Mathematics Subject Classification ID: 35-06
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 58E12
Mathematics Subject Classification ID: 35J48
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 49Q10
zbMATH DE Number: 6657960
MaRDI profile type: Publication
Wikidata QID: Q123256055
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description: scientific article; zbMATH DE number 6657960