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, 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.
Original languageEnglish
Pages (from-to)1159-1164
JournalComptes Rendus Mathematique
Volume347
Issue number19-20
DOIs
Publication statusPublished - Oct 2009

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