Application of Chern-Simons gauge theory to the enclosed volume of constant mean curvature surfaces in the 3-sphere

Lynn Heller, Sebastian Heller, Martin Traizet

Building on Hitchin's work of the Wess-Zumino-Witten term for harmonic maps into Lie groups, we derive a formula for the enclosed volume of a compact CMC surface $f$ in $\mathbb S^…