Wente torus

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An immersed Wente torus is a doughnut-shaped surface in 3D space where the mean curvature is the same at every point. It was discovered by Henry C. Wente in 1986. This surface shows that Hopf’s idea—that all closed, compact constant-mean-curvature surfaces must be spheres—is false for immersed surfaces. The rule holds if the surface is embedded (no self-intersections). Similar constant-mean-curvature examples exist for every positive genus.