The Willmore Conjecture for immersed tori with small curvature integral

Details The Willmore Conjecture for immersed tori with small curvature integral The Willmore Conjecture for immersed tori with small curvature integral

1999-06-10

arxiv.org/abs/math/9906065v2

Manuscripta Math. 101, no. 1, 1-22 (2000)

Mathematics

Differential Geometry

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

Scientific paper

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

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