The Willmore Conjecture for immersed tori with small curvature integral

Abstract

The Willmore conjecture states that any immersion F:T^2 -> R^n of a 2-torus into flat euclidean space satisfies ${\int }_{T^2}{H}^2\ge 2{\pi }^2$. We prove it under the condition that the L^p-norm of the Gaussian curvature is sufficiently small.

26 pages, Latex2e, 3 figures using pstricks, some minor changes, numbers of theorems and propositions changed