Scalar curvature, mean curvature and harmonic maps to the circle

Xiaoxiang Chai; Inkang Kim

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arXiv · 2103.09737

Scalar curvature, mean curvature and harmonic maps to the circle

Xiaoxiang Chai·Inkang Kim

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Abstract

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.

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BibTeX RIS

Xiaoxiang Chai, Inkang Kim. 2021-03-17. Scalar curvature, mean curvature and harmonic maps to the circle. https://arxiv.org/abs/2103.09737

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