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.
Related projects:	Specifický výzkum v odborné a učitelské matematice 2023