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Feb 21, 2020 at 20:23 vote accept Irddo
Feb 17, 2020 at 8:27 comment added Sebastian The proof of the invariance of the Willmore functional under conformal changes of the ambient metric is based on the fact that the oriented normals of the surface with respect to two conformal metrics are scalings of each other.
Feb 14, 2020 at 8:27 comment added Irddo big thanks for your comments. Do you have any information about the normal vector field? Because, when $\Sigma$ is oriented, then we can suppose that the normal of the two immersion are the same, I guess.
Feb 13, 2020 at 16:18 history answered Sebastian CC BY-SA 4.0