Harmonic maps to the circle with higher dimensional singular set

Marco Badran (ETH, Zurigo)
Harmonic maps to the circle with higher dimensional singular set

Abstract
We consider the problem of finding harmonic maps to the circle with a prescribed singular set in an arbitrary Riemannian manifold and characterise their uniqueness in terms of the "one-dimensional topology" of the ambient space. We then show how these maps can be used to define new notions of (n-2)-volume, leading to a promising approximation scheme for classical codimension 2 minimal surfaces.