Lower bound for energies of harmonic tangent unit-vector fields on convex polyhedra

Abstract

We derive a lower bound for energies of harmonic maps of convex polyhedra in ${\mathbb{R}}^3$ to the unit sphere $S^2,$ with tangent boundary conditions on the faces. We also establish that $C^{\infty }$ maps, satisfying tangent boundary conditions, are dense with respect to the Sobolev norm, in the space of continuous tangent maps of finite energy.

Acknowledgment added, typos removed, minor corrections

References in corpus (1)

• Classification of unit-vector fields in convex polyhedra with tangent boundary conditions

Cited by in corpus (4)

• Energies of S^2-valued harmonic maps on polyhedra with tangent boundary conditions
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• Homotopy classification of director fields on polyhedral domains with tangent and periodic boundary conditions, with applications to bi-stable post-aligned liquid crystal displays
• Tangent unit-vector fields: nonabelian homotopy invariants and the Dirichlet energy