Willmore Conjecture
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High Quality Content by WIKIPEDIA articles! In mathematics specifically, in differential geometry the Willmore conjecture is a conjecture about the Willmore energy of a torus. The conjecture is named after the English mathematician Tom Willmore. It is not hard to prove that the Willmore energy satisfies W(M) 4 , with equality if and only if M is an embedded round sphere. Calculation of W(M) for a few examples suggests that there should be a better bound for surfaces with genus g(M) 0. In particular, calculation of W(M) for tori with various symmetries led Willmore to propose in 1965 the…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics specifically, in differential geometry the Willmore conjecture is a conjecture about the Willmore energy of a torus. The conjecture is named after the English mathematician Tom Willmore. It is not hard to prove that the Willmore energy satisfies W(M) 4 , with equality if and only if M is an embedded round sphere. Calculation of W(M) for a few examples suggests that there should be a better bound for surfaces with genus g(M) 0. In particular, calculation of W(M) for tori with various symmetries led Willmore to propose in 1965 the following conjecture, which now bears his name: for any smooth immersed torus M in R3, W(M) 2 2.