Champs de vecteurs unités tangents: invariants homotopiques non abelien et énergie de Dirichlet

Translated title of the contribution: Tangent unit-vector fields: nonabelian homotopy invariants and the Dirichlet Energy

Apala Majumdar, J. M. Robbins, Maxim Zyskin

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Let 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, Ɛ(H) , for continuous tangent maps of arbitrary homotopy type H. The expression for Ɛ(H) involves a topological invariant – the spelling length – associated with the (nonabelian) fundamental group of the n-times punctured two-sphere, pi1(s2 - {s1,...,sn}, *). These results have applications for the theoretical modelling of nematic liquid crystal devices.
Translated title of the contributionTangent unit-vector fields: nonabelian homotopy invariants and the Dirichlet Energy
Original languageFrench
Pages (from-to)1159-1164
Number of pages6
JournalComptes Rendus Mathematique
Volume347
Issue number19-20
DOIs
Publication statusPublished - 25 Sep 2009

Keywords

  • partial differential equations
  • topology

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