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

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

2004-06-01

arxiv.org/abs/math-ph/0406005v2

Lett.Math.Phys. 70 (2004) 169-183

Physics

Mathematical Physics

Acknowledgment added, typos removed, minor corrections

Scientific paper

10.1007/s11005-004-4295-2

We derive a lower bound for energies of harmonic maps of convex polyhedra in
$ \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.

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