A conjectura de Willmore: um caso particular - Douglas Claiton dos Passos Freitas (2013)
In this paper, we prove a particular case of Willmore conjecture, for torus M E3 embedded in Euclidean space E3 as tubes of constant circular sections. For this, we study some properties of the Willmore energy functional, given by W(M) = Z M H2dS. We prove that it is invariant under conformal transformations of Euclidean space E3, and we also prove that the condition for which the integral above, given to normal variationsof immersions of the compact orientable surface M E3 in E3, is stationary is called Euler equation: H + 2H(H2 K) 0.