The Willmore Conjecture for immersed tori with small curvature integral
by
Bernd Ammann

The Willmore Conjecture for immersed tori with small curvature integral (.dvi , .ps, .ps.gz oder .pdf)
Manuscripta Math. 101, no. 1, 1-22 (2000)

Abstract

The Willmore conjecture states that any immersion F:T2-> Rn of a 2-torus into euclidean space satisfies \int_{T2} H2\ge 2\pi2. We prove it under the condition that the Lp-norm of the Gaussian curvature is sufficiently small.

Mathematics Subject Classification

53A05 (Primary), 53A30, 58G30 (Secondary)

Keywords

Willmore integral, conformal metrics, two-dimensional torus
Bernd Ammann, 12.10.1999