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Counterexample to a conjecture of H. Hopf
Pacific Journal of Mathematics
The purpose of this paper is to produce an immersion of a compact oriented two-dimensional surface of genus one into Euclidean 3-space with constant mean curvature H Φ 0. We thus provide a counterexample in dimension 3 to the following conjecture of H. Hopf. / / KdA = I I sinhωcoshω dudv J ^[Ω + (λ)] J J Ω + (λ) = [ f sinh Wcosh W(2λ) dudv = -( ί ΔWdu dv J Jdoi:10.2140/pjm.1986.121.193 fatcat:vjiig4ljfnctde6xxoharytpdm