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dc.contributor.authorMajumdar, Apala
dc.contributor.authorRobbins, J.M.
dc.contributor.authorZyskin, Maxim
dc.date.accessioned2016-02-28T06:31:11Z
dc.date.available2016-02-28T06:31:11Z
dc.date.issued2009-10
dc.identifier.citationMajumdar A, Robbins JM, Zyskin M (2009) Tangent unit-vector fields: Nonabelian homotopy invariants and the Dirichlet energy. Comptes Rendus Mathematique 347: 1159–1164. Available: http://dx.doi.org/10.1016/j.crma.2009.09.002.
dc.identifier.issn1631-073X
dc.identifier.doi10.1016/j.crma.2009.09.002
dc.identifier.doi10.1016/S0252-9602(10)60131-2
dc.identifier.urihttp://hdl.handle.net/10754/599864
dc.description.abstractLet O be a closed geodesic polygon in S2. Maps from O into S2 are said to satisfy tangent boundary conditions if the edges of O are mapped into the geodesics which contain them. Taking O to be an octant of S2, we evaluate the infimum Dirichlet energy, E (H), for continuous tangent maps of arbitrary homotopy type H. The expression for E (H) involves a topological invariant - the spelling length - associated with the (nonabelian) fundamental group of the n-times punctured two-sphere, π1 (S2 - {s1, ..., sn}, *). These results have applications for the theoretical modelling of nematic liquid crystal devices. To cite this article: A. Majumdar et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). © 2009 Académie des sciences.
dc.description.sponsorshipA.M. is supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) to the Oxford Centre for Collaborative Applied Mathematics (OCCAM). We thank Ulrike Tillmann for stimulating discussions and we thank Cameron Hall for help with the French summary.
dc.publisherElsevier BV
dc.titleTangent unit-vector fields: Nonabelian homotopy invariants and the Dirichlet energy
dc.typeArticle
dc.identifier.journalComptes Rendus Mathematique
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdom
dc.contributor.institutionUniversity of Bristol, Bristol, United Kingdom
dc.contributor.institutionDepartment of Mathematics, Brownsville, TX 78520, United States
kaust.grant.numberKUK-C1-013-04


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