A sharp characterization of the Willmore invariant

• Autoři: BLITZ Samuel Harris
• Rok publikování: 2023
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: International Journal of Mathematics
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• www: https://doi.org/10.1142/S0129167X23500544
• Doi: http://dx.doi.org/10.1142/S0129167X23500544
• Klíčová slova: Extrinsic conformal geometry; hypersurface embeddings; Willmore invariant
• Popis: 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.

Související projekty

• Specifický výzkum v odborné a učitelské matematice 2023