Energies of S^2-valued harmonic maps on polyhedra with tangent boundary conditions

Details Energies of S^2-valued harmonic maps on polyhedra with tangent boundary conditions Energies of S^2-valued harmonic maps on polyhedra with tangent boundary conditions

2006-06-07

arxiv.org/abs/math-ph/0606024v1

Annales Henri Poincare 25, 77 - 103 (2008)

Physics

Mathematical Physics

42 pages, 2 figures

Scientific paper

10.1016/j.anihpc.2006.11.003

A unit-vector field n:P \to S^2 on a convex polyhedron P \subset R^3 satisfies tangent boundary conditions if, on each face of P, n takes values tangent to that face. Tangent unit-vector fields are necessarily discontinuous at the vertices of P. We consider fields which are continuous elsewhere. We derive a lower bound E^-_P(h) for the infimum Dirichlet energy E^inf_P(h) for such tangent unit-vector fields of arbitrary homotopy type h. E^-_P(h) is expressed as a weighted sum of minimal connections, one for each sector of a natural partition of S^2 induced by P. For P a rectangular prism, we derive an upper bound for E^inf_P(h) whose ratio to the lower bound may be bounded independently of h. The problem is motivated by models of nematic liquid crystals in polyhedral geometries. Our results improve and extend several previous results.

Affiliated with

Also associated with

No associations

Rating

Energies of S^2-valued harmonic maps on polyhedra with tangent boundary conditions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Energies of S^2-valued harmonic maps on polyhedra with tangent boundary conditions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Energies of S^2-valued harmonic maps on polyhedra with tangent boundary conditions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-698464