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. To cite this article: A. Majumdar et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). © 2009 Académie des sciences.
Original language | English (US) |
---|---|
Pages (from-to) | 1159-1164 |
Number of pages | 6 |
Journal | Comptes Rendus Mathematique |
Volume | 347 |
Issue number | 19-20 |
DOIs | |
State | Published - Oct 2009 |
Externally published | Yes |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: A.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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.