Bernstein problem

The Bernstein problem asks whether the shape of certain minimal surfaces—surfaces that minimize area while spanning a boundary—must always be a plane. In simpler terms, it explores whether the only smooth, stable surfaces with zero mean curvature (like soap films) bounded by a simple closed curve in three-dimensional space are flat planes. For low-dimensional cases, the answer is yes, but in higher dimensions, the problem becomes more complex, and mathematicians seek to understand whether more intricate minimal surfaces can exist beyond the flat ones.