The Willmore conjecture in the real projective space (Q1574759)

The author proves that for any torus \(M\) immersed in the real projective space \(\mathbb{R} P^3(1)\) with mean curvature \(H\), \(\int_M (1+H^2) dA\geq \pi^2\) holds, with the equality holding only for the minimal Clifford torus. Several interesting applications are also given. Furthermore, the author shows that a Klein bottle with handles cannot be embedded into projective 3-space.