Counterexample to a conjecture of H. Hopf

Henry Wente
1986 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 J
doi:10.2140/pjm.1986.121.193 fatcat:vjiig4ljfnctde6xxoharytpdm