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The Willmore Conjecture for immersed tori with small curvature integral

Bernd Ammann
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Abstract

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

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Bernd Ammann. 1999-11-16. The Willmore Conjecture for immersed tori with small curvature integral. https://arxiv.org/abs/math/9906065

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