The Willmore conjecture in the real projective space (Q1574759)
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scientific article; zbMATH DE number 1489538
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Willmore conjecture in the real projective space |
scientific article; zbMATH DE number 1489538 |
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The Willmore conjecture in the real projective space (English)
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13 August 2000
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The author proves that for any torus \(M\) immersed in the real projective space \(\mathbb{R} P^3(1)\) with mean curvature \(H\), \(\int_M (1+H^2) dA\geq \pi^2\) holds, with the equality holding only for the minimal Clifford torus. Several interesting applications are also given. Furthermore, the author shows that a Klein bottle with handles cannot be embedded into projective 3-space.
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total mean curvature
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Willmore conjecture
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Willmore functional
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minimal Clifford torus
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