The geometric Cauchy problem for the membrane shape equation

We address the geometric Cauchy problem for surfaces associated to the membrane shape equation describing equilibrium configurations of vesicles formed by lipid bilayers. This is the Euler-Lagrange equation of the Canham-Helfrich-Evans elastic curvature energy subject to constraints on the enclosed...

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Bibliographic Details
Published inarXiv.org
Main Authors Jensen, Gary R, Musso, Emilio, Nicolodi, Lorenzo
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 06.10.2014
Subjects
Cauchy problems
Curvature
Euler-Lagrange equation
Lipids
Mathematics - Differential Geometry
Mathematics - Mathematical Physics
Physics - Mathematical Physics
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ISSN2331-8422
DOI10.48550/arxiv.1406.5981

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Summary:We address the geometric Cauchy problem for surfaces associated to the membrane shape equation describing equilibrium configurations of vesicles formed by lipid bilayers. This is the Euler-Lagrange equation of the Canham-Helfrich-Evans elastic curvature energy subject to constraints on the enclosed volume and the surface area. Our approach uses the method of moving frames and techniques from the theory of exterior differential systems.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1406.5981