Scalar curvature, mean curvature and harmonic maps to the circle

Xiaoxiang Chai, Inkang Kim

Published 2021-03-17Version 1

We study harmonic maps from a 3-manifold with boundary to $\mathbb{S}^1$ and prove a special case of dihedral rigidity of three dimensional cubes whose dihedral angles are $\pi / 2$. Furthermore we give some applications to mapping torus hyperbolic 3-manifolds.