S. M. Cherosova, E. I. Shamaev, “On Willmore Surfaces of Revolution in <nobr>$\mathbb{R}^3$</nobr>”, Sib. Èlektron. Mat. Izv., 2014, Volume 11,Pages <nobr>887

Geometry and topology

On Willmore Surfaces of Revolution in $\mathbb{R}^3$

S. M. Cherosova^a, E. I. Shamaev^ba

^a Research Institute of Mathematics of North-Eastern Federal University named after M. K. Amosov
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: In this paper, we study Euler–Lagrange equation for the Willmore functional in the case of surfaces of revolution. Explicit solutions are constructed in terms of elliptic functions.

Keywords: Willmore surface, exact solution.

UDC: 514.74

MSC: 52C05

Received November 14, 2014, published December 1, 2014