A sharp characterization of the Willmore invariant

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Authors

BLITZ Samuel Harris

Year of publication 2023
Type Article in Periodical
Magazine / Source International Journal of Mathematics
MU Faculty or unit

Faculty of Science

Citation
Web https://doi.org/10.1142/S0129167X23500544
Doi http://dx.doi.org/10.1142/S0129167X23500544
Keywords Extrinsic conformal geometry; hypersurface embeddings; Willmore invariant
Description First introduced to describe surfaces embedded in R3, the Willmore invariant is a conformally-invariant extrinsic scalar curvature of a surface that vanishes when the surface minimizes bending and stretching. Both this invariant and its higher-dimensional analogs appear frequently in the study of conformal geometric systems. To that end, we provide a characterization of the Willmore invariant in general dimensions. In particular, we provide a sharp sufficient condition for the vanishing of the Willmore invariant and show that in even dimensions it can be described fully using conformal fundamental forms and one additional tensor.
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