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Tag: conformal-geometry

Demystification of the Willmore integrand

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 …

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Posted by rodion n. déevApril 16, 2021Posted in differential geometryLeave a comment on Demystification of the Willmore integrand