TY - JOUR
T1 - New Developments on the p-Willmore Energy of Surfaces
AU - Aulisa, Eugenio
AU - Gruber, Anthony
AU - Toda, Magdalena
AU - Tran, Hung
N1 - Publisher Copyright:
© 2020 Bulgarian Academy of Sciences. All rights reserved.
PY - 2020
Y1 - 2020
N2 - The p-Willmore energy Wp, which extends the venerable Willmore energy by accommodating different powers of the mean curvature in its integrand, is a relevant geometric functional that bears both similarities and differences to its namesake. To elucidate this, some recent results in this area are surveyed. In particular, the first and second variations of Wp are given, and a flux formula is presented which reveals a connection between its critical points and the minimal surfaces. Finally, a model for the p-Willmore flow of graphs is presented, and this connection is visualized through computer implementation.
AB - The p-Willmore energy Wp, which extends the venerable Willmore energy by accommodating different powers of the mean curvature in its integrand, is a relevant geometric functional that bears both similarities and differences to its namesake. To elucidate this, some recent results in this area are surveyed. In particular, the first and second variations of Wp are given, and a flux formula is presented which reveals a connection between its critical points and the minimal surfaces. Finally, a model for the p-Willmore flow of graphs is presented, and this connection is visualized through computer implementation.
KW - Curvature functionals
KW - Minimal surfaces
KW - Willmore energy
KW - Willmore flow
UR - http://www.scopus.com/inward/record.url?scp=85104136038&partnerID=8YFLogxK
U2 - 10.7546/giq-21-2020-57-65
DO - 10.7546/giq-21-2020-57-65
M3 - Article
AN - SCOPUS:85104136038
SN - 1314-3247
VL - 21
SP - 57
EP - 65
JO - Geometry, Integrability and Quantization
JF - Geometry, Integrability and Quantization
ER -