conformal-geometry Archives

The Willmore energy for a surface $S$ in Euclidean 3-space is defined as $\tilde{W}(S) = \int_S \mu^2\omega_S$ , where $\mu$ is the mean curvature of $S$ and $\omega_S$ its area form. It’s known to be invariant under the conformal transformations (whereas the mean curvature itself is not). White, and later Bryant noticed that the 2-form $\Omega_S = (\mu^2-K)\omega_S$ , where $K$ stands …