## 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, 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.

Translated title of the contribution | Tangent unit-vector fields; nonabelian homotopy invariants and the Dirichlet energy |
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Original language | English |

Pages (from-to) | 1159 - 1164 |

Number of pages | 6 |

Journal | Comptes Rendus Mathematique |

Volume | 347 |

Issue number | 19-20 |

DOIs | |

Publication status | Published - Oct 2009 |