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@article{2304043,
author = {Blitz, Samuel Harris},
article_number = {9},
doi = {http://dx.doi.org/10.1142/S0129167X23500544},
keywords = {Extrinsic conformal geometry; hypersurface embeddings; Willmore invariant},
language = {eng},
issn = {0129-167X},
journal = {International Journal of Mathematics},
title = {A sharp characterization of the Willmore invariant},
url = {https://doi.org/10.1142/S0129167X23500544},
volume = {34},
year = {2023}
}
TY - JOUR
ID - 2304043
AU - Blitz, Samuel Harris
PY - 2023
TI - A sharp characterization of the Willmore invariant
JF - International Journal of Mathematics
VL - 34
IS - 9
SP - 1-32
EP - 1-32
PB - World Scientific Publishing
SN - 0129167X
KW - Extrinsic conformal geometry
KW - hypersurface embeddings
KW - Willmore invariant
UR - https://doi.org/10.1142/S0129167X23500544
N2 - 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.
ER -
BLITZ, Samuel Harris. A sharp characterization of the Willmore invariant. \textit{International Journal of Mathematics}. World Scientific Publishing, 2023, roč.~34, č.~9, s.~1-32. ISSN~0129-167X. Dostupné z: https://dx.doi.org/10.1142/S0129167X23500544.
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