Constant-angle surfaces in liquid crystals

Abstract

We discuss some properties of surfaces in R3 whose unit normal has constant angle with an assigned direction field. The constant angle condition can be rewritten as an Hamilton-Jacobi equation correlating the surface and the direction field. We focus on examples motivated by the physics of interfaces in liquid crystals and of layered fluids, and discuss the properties of the constant-angle surfaces when the direction field is singular along a line (disclination) or at a point (hedgehog defect