Willmore conjecture

The Willmore conjecture is a mathematical statement about the shape of surfaces, specifically tori (donut-shaped surfaces). It asserts that among all tori with a fixed size, the one with the smallest "bending energy" (measured by a quantity called the Willmore energy) has a specific shape called the Clifford torus. This shape evenly distributes curvature and minimizes bending. In 2012, mathematician Fernando Coda Marques and André Neves proved the conjecture, showing that the Clifford torus indeed has the minimal bending energy among all tori of the same size.