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ON THE WILLMORE FUNCTIONAL OF 2-TORI IN SOME PRODUCT RIEMANNIAN MANIFOLDS
Published online by Cambridge University Press: 30 March 2012
Abstract
We discuss the minimum of Willmore functional of torus in a Riemannian manifold N, especially for the case that N is a product manifold. We show that when N = S2 × S1, the minimum of W(T2) is 0, and when N = R2 × S1, there exists no torus having least Willmore functional. When N = H2(−c) × S1, and x = γ × S1, the minimum of W(x) is .
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- Research Article
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- Copyright © Glasgow Mathematical Journal Trust 2012
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