TY - JOUR

T1 - New Developments on the p-Willmore Energy of Surfaces

AU - Aulisa, Eugenio

AU - Gruber, Anthony

AU - Toda, Magdalena

AU - Tran, Hung

PY - 2000

Y1 - 2000

N2 - The p-Willmore energy W^p, 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 W^p 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 W^p, 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 W^p 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.

M3 - Article

SP - 57

EP - 65

JO - Geometry, Integrability & Quantization (Journal of Geometry and Physics Edit. Board)

JF - Geometry, Integrability & Quantization (Journal of Geometry and Physics Edit. Board)

ER -