English

The Willmore Conjecture for immersed tori with small curvature integral

Differential Geometry 2007-05-23 v2

Abstract

The Willmore conjecture states that any immersion F:T^2 -> R^n of a 2-torus into flat euclidean space satisfies T2H22π2\int_{T^2} H^2\geq 2\pi^2. We prove it under the condition that the L^p-norm of the Gaussian curvature is sufficiently small.

Keywords

Cite

@article{arxiv.math/9906065,
  title  = {The Willmore Conjecture for immersed tori with small curvature integral},
  author = {Bernd Ammann},
  journal= {arXiv preprint arXiv:math/9906065},
  year   = {2007}
}

Comments

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