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.

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